Talk:Approval voting

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Replace the dead link with this link to the American Stats Association bylaws: http://www.amstat.org/about/bylaws.cfm —Preceding unsigned comment added by 96.49.251.87 (talk) 14:17, 14 July 2010 (UTC)

"Dichotomous preferences", "arbitary cutoff" & Problematic chart

This part of the article makes no sense to someone who doesn't know what "Dichotomous preferences" means. It is not defined, and it's not obvious to know what it means through internet searches.

<<Dichotomous preferences Approval voting avoids the issue of multiple sincere votes in special cases when voters have dichotomous preferences. For a voter with dichotomous preferences, approval voting is strategy-proof (also known as strategy-free).[29] When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval voting is guaranteed to elect the Condorcet winner, if one exists.[30] However, having dichotomous preferences when there are three or more candidates is not typical. It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters.[25] Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group.[31] A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences. Being strategy-proof for a voter means that there is a unique way for the voter to vote that is a strategically best way to vote, regardless of how others vote. In approval voting, the strategy-proof vote, if it exists, is a sincere vote.[24>>

Then, in the criteria, it has a whole category of approval voting magically meeting all listed criteria when voters have dichotomous preferences, as compared to other forms of approval voting. But the article should evaluate criteria based on approval voting as a single concept, not with contingencies that don't exist in the real world. RRichie (talk) 12:28, 26 June 2011 (UTC)

I'm not sure why you're saying dichotomous preferences aren't defined, since you quoted the paragraph that contains a definition ("Having dichotomous preferences means... ...does not have dichotomous preferences."). Could you please clarify?

As for the criteria table, I don't see that it makes much difference how many voter models are considered during analysis. So long as it's clear which model is realistic for a given situation, additional models simply contribute to the explanation of the theory, which includes, but is not limited by, the details of practical application. That said, I suppose there is some question of notability, and I'm not familiar with how exactly that should be applied to article content. Douglas Cantrell (talk) 07:00, 30 June 2011 (UTC)

You're correct, this unusual term is defined jere, although not in a very obvious way -- e.g., well after it is introduced. More broadly, however, you talk of "special cases when voters have dichotomous preferences." That's so unlikely to be a reality in the real world, that it seems odd to then present this situation as an intrinsic way to evaluate the method -- indeed on an equal basis with approval voting as a basic system. But it seems like the system as it really might be used in a full range of candidate scenarios, deserves to be treated quite differently than esoteric, angels-on-a-pin-type discussion of "in the event of this highly unusual, unrealistic theoretical situation, this is how the system handles different criteria.

In other words, if I were student or policymaker trying to understand the system and how it compares to other systems, this presentation of criteria would be quite confusing and likely misleading.RRichie (talk) 12:41, 2 July 2011 (UTC)

I too have real objections to that chart. If approval voting fails a criterion under any strategic voting regime then it fails that criteria as a whole, and that chart does not make that clear at all. Under a strong Nash equilibrium plurality voting passes the majority and Condorcet criteria, yet the system as a whole fails them both. Almost any system can produce the Condorcet winner - it only passes the Condorcet criteria if the system must always produce the Condorcet winner. This chart should properly show approval voting failing the Majority, Constitency & Participation, Condorcet, Condorcet Loser, and Independence of Irrelevant Alternatives criteria (assuming that the chart is accurate currently, which I'm not sure it is especially on the last one). RMCampbell (talk) 21:07, 16 November 2011 (UTC)

Q1: Given the “dichotomous preference” scenario is “not typical” and “unlikely” as stated in the article, then why is it listed first in the table, above the mathematical compliance (i.e. arbitrary cutoff)? Shouldn’t it be listed last, if at all? Doesn’t this reflect an obvious bias in the article and weaken the article?

It seems to me the only logical possible dichotomous preference scenario is one which the options (or candidates) are completely polarized while candidates belonging to the same pole are also perfect clones. In other words, for any non-trivial (i.e. three option) election over A B C, if there exists a block of voters that all prefer A>C then all such voters must place B either on the side of A exclusively, or C exclusively (you cannot have some A>C voters placing B on one pole and some on the other). This scenario seems so statistically impossible it may effectively never occur in nature for any candidate election, because even two candidates on the same pole will have an incentive to distinguish themselves (in fact one could argue this is why more than one candidate emerges on a given pole. e.g. “left” or “right” because there is more than one distinct flavor of “left” or “right.) Thus, the only dichotomous preference scenario I can possibly imagine in the real world would be not an election for candidates, but other goods (or available options), that might be cloned or have uniform equal utility to one set of divided voters, and uniform polar opposite utility to another set.

Q2: Is there any remotely realistic example of inherently dichotomous preferences in a non-trivial election? There are certain statistical boundaries in nature that are 100% reliable, for example graphing the heights of individuals in a given population produces something resembling a bell curve, every time, and will never produce a saw-tooth. Is there any inherently dichotomous preference scenario that can occur in nature, at all?

Filingpro (talk) 10:01, 18 May 2013 (UTC)

I propose we remove all mention of “dichotomous preference” from the article. As mentioned, it is a wholly unrealistic situation that will never occur in practice, so the discussion of it takes the article on a theoretical tangent that has no bearing on the actual use and merits of approval voting. Qaanol (talk) 00:55, 2 February 2014 (UTC)

IIA and clone immunity assuming arbitrary cutoff

I'm fairly certain approval voting satisfies both criteria when the voter model is arbitrary cutoff, but the criteria table said that it fails both. Since the articles on those criteria specifically list approval voting as being a method which satisfies them, I've changed the table to reflect my current understanding. If I'm mistaken, I would appreciate a source that shows that approval fails those criteria. If none can be found, I would request that the table be modified to reflect the ambiguity of the situation while I look for a reliable source myself.

Also, I get the feeling this is going to come up: The addition of a candidate to a race can cause a change in the strategic situation, which can alter how people vote, which can in turn modify the outcome of an election, even if the new candidate is not the new winner. This is not, however, a violation of IIA. I'm not aware of any non-trivial method that would satisfy IIA if that were the case. IIA is only violated if the outcome is changed despite votes remaining the same, with the obvious exception of the removed candidate. Douglas Cantrell (talk) 07:38, 30 June 2011 (UTC)

@Cantrell. Thank you for you collaborative posting. No doubt Approval voting is resistant to spoiler effects, while I'm sure you would agree it is clearly not immune.

Yes I do understand your point, although here is the problem I see.

Suppose:

ELECTION 1: C WINNER

3 C

2 A (Voters prefer A > B > C)

2 B

ELECTION 2: B WINNER (ELIMINATE IRRELEVANT ALTERNATE A)

3 C

4 B

I understand your point that, in order to show IIA failure, we have changed the voting between B & C, according to the markings on the approval ballots. But I believe the correct test is merely whether we change the voter preferences, which we have not. The reason is that a vote "A" can mean, mathematically that B > C, possibly, for the voter. This is because the mechanism of an approval ballot does not record relative preferences between either all approved or all unapproved candidates. If we adopt a mathematical model without voter preferences then we are no longer creating a model of the very subject matter at hand - that is group decision theory (i.e. the single-winner problem).

I believe the essence of IIA is that if B > C by a voting rule, then adding A shouldn't change to C > B if the voters preferences between other candidates (other than A) do not change. Approval with arbitrary cutoff fails this criterion as proven in the above example.

Filingpro (talk) 00:00, 18 May 2013 (UTC)

In your example, two voters moved their approval cutoff when A was eliminated. If their cutoff was arbitrary, there would be no reason to do that.

If you want to make a row on the table for optimal strategy with imperfect information, I wouldn't object to having 'No' in the IIA column. I wouldn't necessarily agree with it either, but I'm no longer confident that I fully understand how IIA is defined. Douglas Cantrell (talk) 22:51, 6 June 2013 (UTC)

If the cutoff is arbitrarily decided by the voter, we cannot presume to know how the decision is made, and therefore we cannot assume the cutoff cannot be affected by the available candidates.

I believe the model you imply violates democratic principles Non-Dictatorship and Pareto Efficiency.

To guarantee the voter’s cutoff to remain fixed when available candidates change, (1) the cutoff must be determinable on an absolute scale independently and prior to knowing any available candidates, and (2) candidates must also be rated on the absolute scale. These requirements are not stipulated explicitly in the article.

Yes I agree with your suggestion to add “imperfect information” model. Thanks. (Please see Compliance Proposal... further below.)

Filingpro (talk) 05:04, 10 October 2013 (UTC)

Inclusion of "Sincere" Voting Without "Later-No-Harm" Leads To Contradiction & Bias

This article is unacceptably inconsistent.

The article includes a section on "sincere" voting which asserts according to approval experts that for a single voter, both of the following ballots can be concurrently sincere votes (an election with candidates A B C):

A

and

A B

These cannot logically be concurrently sincere votes unless A > B > C, AND WE DO NOT CONSIDER “A B” TO BE EQUAL PREFERENCES. If you consider “A B” to be equal =, then ballot “A” cannot logically be a sincere vote because then A > B, which leads to a contradiction.

The article includes an entire section and numerous references to “sincere” voting based on understanding approval voting through the prism of a voter’s ordinal preferences (as stated in the article).

The contradiction in the article occurs through the selective omission of the “Later-No-Harm” criterion (in the comparison chart for this article). Approval voting’s failure of the criterion is essential to understanding one of its primary strategic voting flaws: Bullet Voting.

We cannot say on the one hand that every approval vote is “sincere” based on ordinal preferences, and then on the other hand disregard the application and failure of “Later-No-Harm” criterion on the basis that Approval cannot be understood through ordinal frameworks, when it can. This is a glaring contradiction and reflects a bias in the article.

Filingpro (talk) 20:01, 17 May 2013 (UTC)

Compliance Proposal Disclosing Failure of Democratic Criteria

See also prior discussion IIA and clone immunity assuming arbitrary cutoff

PROPOSAL

(added criteria)

• Non-dictatorship —The election can not be decided by a single voter without considering all voters.
• Pareto Efficiency —If every voter prefers candidate A to all other candidates, then A must be elected. (from Arrow's impossibility theorem)

		Non-dictatorship	Pareto Efficiency	Majority	Monotone	Consistency & Participation	Condorcet	Condorcet loser	IIA	Clone independence	Reversal symmetry
All voters	Voter absolute cutoff (independent of available candidates)	No	No	No	Yes	Yes	No	No	Yes	Yes	Yes
	Voter average utility	Yes	Yes	No	Yes	Yes	No	No	No	No	Yes
	Strategy with imperfect information about other voters	Yes	Yes	No	Yes	No	No	No	No	No	Yes
	Strong Nash equilibrium (Perfect information, rational voters, and perfect strategy)	Yes	Yes	Yes	Yes	No	Yes	No	No	Yes	Yes
Conforming voters only	Inherently dichotomous preferences	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes

REASONING

1. Non-dictatorship and Pareto

We must disclose if a proposed model violates basic axioms of democracy.

2. “Arbitrary cutoff” changed to “Voter absolute cutoff”

Arbitrary implies movable:

“having only relative application or relevance; not absolute”
“not representing any specific value”
“subject to individual discretion, whim, convenience, impulse, will, preference”
“not following a consistent rule, unrestrained, unrestricted, unpredictable, unreasonable, seemingly random”
(compiled from http://www.thefreedictionary.com/arbitrary and http://www.merriam-webster.com/dictionary/arbitrary)

Note: We cannot assume the voter picks a cutoff relative to any arbitrary candidate without the logical consequence that the cutoff might change when other candidates are introduced.

I would be happy to use “arbitrary cutoff” if there is a formal definition and a citation for IIA.

3. Average utility
A non-dictatorial model that does not involve strategy about other voters preferences is very useful here. Note: this voter model is demonstrated in the Memphis example earlier in the article and so improves consistency.

4. Imperfect information
Nearest to the general case for approval voting and therefore essential.

5. Column for Voter Exclusion
Dichotomous preferences necessitates excluding voters for holding certain opinions which is categorically different than any other “cutoff” model and therefore is a special case. This clarification helps the reader to understand and compare cutoff models (i.e. “apples to apples”).

6. Sorting
In order of increasing strategy relative to available candidate utilities and then incorporating other voter preferences

7. Compliance
Voter absolute cutoff violates Pareto because if all voters prefer A>B but their absolute cutoff is above both they can’t elect A unambiguously, they can only elect the tie. Likewise Non-dictatorship is violated because if we add a single voter with preference B>A with absolute cutoff between B and A, this voter becomes the dictator.

Dichotomous Preferences violates Non-dictatorship because if voter V1 prefers A>B>C while V2 prefers C >A=B then V1 is excluded from the election arbitrarily and V2 is the dictator.

Average utility fails Clone independence:
2: AB (A:100, B:55, C:0)
1: B (B:100, C:25, A:0)
CLONE A to change winner from B to A.

Other compliances are adapted from the current table. Citations are welcomed.

Open to improvements and suggestions before posting...
Filingpro (talk) 05:16, 10 October 2013 (UTC)

After several weeks, posted.
Filingpro (talk) 02:22, 29 October 2013 (UTC)

Non-dictatorship means that there isn't a single voter that always decides the outcome, not that the outcome is never decided by a single voter. You can see a formal definition by Kenneth Arrow here. (Page 9.) Since every non-trivial voting system satisfies the criterion, I see little value in including it. Also, a voter that prefers A>B>C is impossible given dichotomous preferences.

I'm not convinced that 'absolute cutoff' is the best name for that voter model. Even if it's interpreted as 'unconditional cutoff' rather than 'total cutoff,' it doesn't explain what it means to be unconditional, or give any insight into how the cutoff was chosen. Even a note saying 'independent of available candidates' doesn't seem very clear. I'd suggest 'random cutoff,' but I suppose it's best to keep things deterministic. Perhaps 'zero strategy'?

Pareto efficiency (if we're talking about what's defined here) can only fail if there's a tie, and only if literally none of the voters put their approval cutoff between the two options. Still failure if you're looking at voter preferences rather than expressed preferences, but I think a footnote like the one for the condorcet loser criterion might be warranted. Also, average utility fails if absolute cutoff does; 3: AB (A:100, B:80, C:0) is an example where A and B tie even though every voter prefers A.

I'm fairly confident that optimal strategy with limited information satisfies participation. Also, I don't think any of the voter models can be said to include 'all voters.' They all exclude anyone that doesn't conform to the model, whether that model is based on strategic behavior, levels of knowledge, or resolution of preferences. Douglas Cantrell (talk) 10:08, 5 November 2013 (UTC)

No comments for two weeks, so I tried to fix the things that I believe to have been mistakes. Also tried to clean up the categories a bit, but that may be something that requires more discussion. I'll be checking back here every few days for at least another two weeks in case someone has comments. Douglas Cantrell (talk) 07:04, 20 November 2013 (UTC)

First, thanks for fixes on items overlooked:
- failure of Pareto by average utility
- I agree we are allowed to imagine a dichotomous preference society prior to labeling it dictatorship (although concerns over relevance remain)

Participation & Imperfect Information:
-Markus Schulze posted in Archive 3 that Condorcet and Participation are incompatible, so there is no issue there. How is it that under Nash E with perfect information failure occurs and does not with imperfect information? I don't know the mechanism. Could it be that participating causes another voter to cast a counter-vote or withdraw an approval that results in a tie?

Items to reach agreement on, or find sources:
-dictatorship of IIA compliant cutoff models
-defining "sincere" or "zero strategy" cutoff model, if it exists?

Some of the responses below are long form (some appear to be "proofs"). I believe they may be helpful and I see no harm in including them on the talk page. Meanwhile, we can look for citations.

WHY APPROVAL CUTOFF MODELS WHICH ARE IIA-COMPLIANT ARE DICTATORIAL
Only one failure case is needed for mathematical non-compliance, while failure need not be shown in all cases. Arrow's dictatorship says "for all [alternatives] x and y". We therefore can consider a "society" (from Arrow) confronted with two alternatives. Likewise Arrow stipulates "n” number of voters, so we can consider two voters (n = 2). If we show a voting system provides arbitrary power to a first voter over a second voter, such that the first voter's preference among all available alternatives always wins regardless of the second voter's preference, then we have proven Arrowan dictatorship.

Consider:
1. Voter V1 has preferences a>[b?c] and approves only ‘a’. We can posit such a voter who has some unknown ordinal preference between 'b' and 'c' (either b>c, or c>b), while preferring 'a' to both.
2. To satisfy Independence of Irrelevant Alternatives (IIA), we necessarily adopt an approval cutoff regime C such that voter V1 must approve neither 'b' or 'c' regardless of whether any other alternatives exist. (We know that candidate 'a' need not exist as a necessary condition for C to forbid V1 from approving either 'b' or 'c', because if C satisfies IIA, the existence of candidate 'a' has no effect on V1's cutoff between 'b' and 'c'.)
3. Now consider a society consisting of voter V1 and V2 choosing amongst alternatives 'b' and 'c', with dictator V2 approving only 'b', or only 'c'. Under regime C, V2's preferences will always dictate the outcome regardless of the preferences of V1, because regime C does not permit V1 to approve a more preferred candidate. Hence, V2 is the Arrowan dictator. By this reasoning any approval cutoff model that satisfies IIA is dictatorial.
Note: If we try to counter-argue that another voter V3 exists under regime C that may approve of either 'b' or 'c' to overturn dictator V2, this point is irrelevant because V1 still can exist, and so is the possibility of a society with only V1 and V2.

HOW DO WE DEFINE "SINCERE" VOTING?
If my preferences are (A:100, B:72, C:37, D:12), what is my sincere vote? I don't know.
Note: the literal word 'approval' has no intrinsic meaning to the voting method, which merely stipulates to vote for any number of alternatives, and elects the one with the most votes.
We might try to define a special case where a voter has an acceptability threshold, though I am not clear how. Does this necessitate strictly a single criteria for the voter that can only be satisfied in a binary fashion? If yes, is this identical to dichotomous preferences? If no, then the voter may have a preference among alternatives either approved or not approved, necessarily based on sincere criteria.

Example:
Suppose options A and B above provide sufficient drinking water for my survival, and C and D death. What if B means I must first endure torture to survive? In the face of uncertainty, I might adopt the binary criterion of survival as my standard, so when voting for A, B, C, or D, I approve A and B. In contrast, if I am the only voter, or have information about other voters aligned with me, I might vote for A only, to avoid torture. Likewise, suppose alternatives C and D are not available. If I vote for A only, is this "sincere" because I do not want torture?
The example illustrates when a discernible acceptability threshold exists in a particular context, the acceptability threshold may change when presented with different alternatives.
Another problem: in the article a "sincere" vote can change because there is no specification as to how the voter decides the cutoff, so it can not satisfy IIA.
In my view the term "sincere" is inherently problematic when both 'a' and 'ab' are sincere approvals. Which is the sincere vote? I would rather say when a voter prefers a>b>c, multiple congruent ballot markings exist, and both 'a' and 'ab' are congruent ballot markings.

Filingpro (talk) 03:05, 30 December 2013 (UTC)

Participation: I don't really understand the perfect-info model well enough to comment. For the imperfect-info model, I've been thinking of it as perfect knowledge about the probability of each pairwise tie, where the probabilities are somehow independent of the voters. Given sincere voters, this implies compliance with Participation, so far as I can imagine. I don't know offhand what the implication of a somewhat more realistic model might be.

Dictatorship: Were your argument sound, would it not follow that all deterministic voting systems are dictatorial, because it's possible to imagine an election with three voters and two candidates where V1 has preference A>B and V2 has preference B>A?

Sincerity: A vote is sincere if every approved candidate is preferred to every disapproved candidate. For any given voter, there are many possible sincere votes; all of the voter models in the current table consist exclusively of sincere voters, so far as I understand.

Zero-Strategy Model: I've been assuming that voters would just choose a random vote from among those possible which happen to be sincere.

As an aside, I'm starting to wonder if it really makes sense to model voters at all. Can't most criteria be understood in terms of the ballots themselves? Douglas Cantrell (talk) 03:08, 2 January 2014 (UTC)

Dictatorship: We agree deterministic voting systems such as Approval, Plurality, IRV etc. are not dictatorial, though certain cutoff models for Approval voting are dictatorial. For three voters and two candidates in Plurality voting, no voter has arbitrary power over another. But for Approval cutoff models where V1 who prefers either A>B or B<A , but cannot approve any, dictator V2 can choose any outcome regardless of the preferences in any order of all other voters (i.e. V1). Approval voting as a general method is not dictatorial because specific cutoff regimes are not intrinsic to the method, but neither does Approval pass IIA.

Sincere Voting: Under the definition the cutoff is mathematically unspecified - "sincere" only means the voter decides in some unspecified way - so we can not assume the decision is made randomly. The problem I see is that the article says "Approval satisfies different criterion based on how the cutoff is chosen" <-- which I think is a good. I think therefore the table should make clear how the cutoff is in fact chosen, which "sincere" does not.

I am open to stipulating "random" but have concerns over relevance, and in order to pass IIA it would have to be clearly defined to be computed on an absolute scale by the voter independent of knowing any candidates, and then it would fail Arrow's non-dictatorship (without objective criteria one voter's perverse recreational interests could have arbitrary power over another voter's sustenance).

PROPOSAL: At the moment my recommendation is we remove "sincere" row and we consider only non-dicatorial cutoff models, then we could eliminate "non-dictatorship". I remain open to comments.

PS: Re: understanding criteria through prism of ballots. Its my belief we would no longer be creating a mathematical model of the subject matter if we remove the model of the voter having preferences. A unified general voter model (i.e. cardinal preferences) allows us to meaningfully compare voting systems performance with criteria.

Filingpro (talk) 07:17, 8 January 2014 (UTC)

Dictatorship: As far as I can tell, your argument is that abstention (i.e. disapproving all candidates) must be possible in any voter model where approval voting satisfies IIA, that it is therefore possible to imagine an election where only one voter does not need to abstain, and that this implies dictatorship. My argument is that the voter model used when evaluating preferential systems mandates sincere voters, that it is therefore possible to imagine an election with three voters where one voter must rank A>B and another must rank B>A, that this would imply dictatorship if your argument were valid, that it does not imply dictatorship, and that your argument is therefore invalid.

Dictatorship continued: My primary objection to your initial argument is actually the one you provided, namely: "another voter V3 exists under regime C that may approve of either 'b' or 'c' to overturn dictator V2". The argumentum ad absurdum above is my response to the preemptive counterargument you made. A secondary objection is that approval voting always satisfies anonymity, regardless of the voter model, and anonymity implies non-dictatorship.

Sincere Voters: You are correct in saying that the voter model for that row isn't well defined. I was mostly just trying to exclude completely absurd models where, for example, approval would fail participation because voters were approving of everyone except their favorite candidate. Trying to be more specific seems somewhat problematic, since that row was meant to replace 'arbitrary cutoff,' which was itself presumably meant to represent the traditional understanding of which criteria approval voting satisfies. I expect that the traditional understanding is based more on ballots than on voter models.

Proposal: I'm hesitant to make this page the only place on the internet where approval voting is said to fail IIA except when Condorcet and Participation are simultaneously satisfied. One alternative might be to have a third preference model: Ordinal preferences with innate approval threshold. That's probably the best way to model the traditional understanding of the method, and it will bring the criteria table closer to the strategy section of the article, which is something that we should probably be working on anyway. Douglas Cantrell (talk) 03:29, 9 January 2014 (UTC)

I will focus on the dictatorship issue first and post later re other issues:
Dictatorship:

1. With voter V1:A>B and V2:B<A with a V3 deciding voter we have no dictatorship because we don't know who the dictator is. To prove dictatorship, we must show the dictator always prevails in the society for any preference the dictator sincerely chooses, despite any preference the other voters sincerely choose. We can not assume V1:A>B, we can only assume V1:A?B.
2. With an IIA compliant approval cutoff, we can posit a voter V1:A?B with cutoff above both A and B. We know this because a voter A>B with cutoff above both exists, and so does a voter B<A with cutoff above both exist.
   

Does that make sense?
Filingpro (talk) 02:35, 10 January 2014 (UTC)

So the idea is that restrictions may be imposed on the choice of an approval threshold to show dictatorship failure, but not on preferences. I suppose that could be said to follow from how IIA compliance is being handled.

In that case, I suppose I'll just say again that anonymity implies non-dictatorship. I don't know to what extent that's really true in this context, since both criteria were defined in terms of preferential systems, but it seems more reasonable than a definition for non-dictatorship which implies failure in any context where sincerity can require that a voter abstains. Douglas Cantrell (talk) 04:44, 10 January 2014 (UTC)

Restriction On Threshold But Not Preferences:

1. Essentially yes - and a good point I think made, that it seems a contradiction. I have considered this, although I think the problem, again, is that in a society with two alternatives (A & B) a voter V1a: A>B with threshold above both, and V1b: B<A with threshold above both, do exist in the mathematical model (where Approval passes IIA). Because they both exist, we can indeed posit, in the abstract, a voter that is strictly either V1a or V1b, that we call V1. That is, V1 is a legitimate mathematical case - i.e. we are allowed to consider either V1a or V1b as a single case. When we do this, this meets Arrow's requirements for dictatorship because we are considering "for every set of orderings in the domain" by a voter V1, i.e. either A>B or B<A, which can have no impact against some other voter V2 who decides the outcome arbitrarily A or B.
2. I can see the objection to this reasoning, because of the assumption that V1's abstention is "sincere". But the problem is that if V1: A>B, then approving A would be sincere, but the cutoff regime forbids it. Sincerity (as defined in the article) is based solely on the voter's ordinal preferences, and has nothing to do with the cutoff. We can not say that "sincerity requires a voter abstains" when approval of A for preference A>B is sincere, according to the definition. Therefore, it is not the sincerity of the voter that forces abstention, it is the dictatorial cutoff regime.
3. The definition of "sincere" in the article describes an unspecified cutoff among some preference order a voter has for some available candidates, for which we have stipulated no assumptions as to how the voter decides it. It is logically impossible to pass IIA when we don't specify how the cutoff is chosen, we have no basis to assume it cannot move.
   

Anonymity: I think you raise a good point it was defined in terms of ordinal preferences. The problem is that in the ordinal voter model, theorists (i.e. Woodall) refer to the literal "ballot" as the voter preferences, because they are unified for preferential ballots. With Approval under certain cutoff regimes, voter V1 (in examples above) essentially has their "ballot" (i.e preferences) ignored, arbitrarily, by the regime. I believe this is a manner of imposing "extraneous information" on the counting of voter preference (i.e. "ballots" in the case of the preferential model). Another way of looking at it from an approval ballot perspective, is that voters are precluded from marking sincere approvals by an extraneous cutoff regime, while others are not, effectively violating the anonymity of voters - i.e. protection from arbitrary differential treatment.

Innate Approval Threshold:

1. Is this proposed voter model the same as dichotomous preferences? How is it different? I think the idea is to combine cardinal preferences and dichotomous preferences together, to say that each voter has both? The contradiction I see is that a voter is granted cardinal criteria on the one hand, but the model simultaneously assumes the voter does not have the same criteria available when voting. For example, V1 has cardinal criteria 'C' on a scale 0 - 100 for pain reduction, and dichotomous criteria 'D' of >=35 acceptability. With two alternatives A:37 and B:100, V1 approves both, because the voter only ever uses criteria 'D'. If the criteria 'C' are never used under any circumstances by the voter, then how are they part of the voter model? It seems to me, this is the same mathematical model as the dichotomous preference voter model, in which each voter votes according to exactly one binary criteria which can not be satisfied to any degree.
2. If innate threshold means the voter still has full cardinal preferences, then we still fail Arrow non-dictatorship when we force IIA compliance.
3. I would like to refer back to earlier comments "HOW DO WE DEFINE 'SINCERE' VOTING?", because it seems to me that "innate" is a renaming of "sincere".

Proposal: Due to WP:OR and I concede I haven't searched the literature further on this topic, here are some suggestions. If we have a citation for IIA passage under the definition of "sincere cutoff" we could add it, despite my objection. Given that, would it be a fair compromise in the meantime to remove the "sincere/innate/absolute cutoff" until we get a citation or can agree on its definition or compliance? Or I might be willing to cooperate in defining it or perhaps include it as another IIA failure model - further discussion required...
Filingpro (talk) 23:54, 10 January 2014 (UTC)

I definitely screwed up when I described abstention as a consequence of sincerity, so I apologize for that. I'll also concede that a subset of possible voters in the zero strategy model is basically being disenfranchised, although it would probably be more precise to say that those voters are modeled such that they choose to disenfranchise themselves. Anyway, I guess the question is whether the possibility of an election where only one voter chooses to express a preference makes a voting system dictatorial under a given model.

Depending on how you define dictatorship, it may or may not. Or you might not get any answer at all, if you're using a definition that isn't sufficiently general. I'm not sure what Arrow's definition implies, and I'm not sure that it matters; he was trying to dismiss trivial counterexamples to a proof about preferential voting systems. We aren't.

Which, I suppose, raises the question that really needs to be answered before we can resolve this: What are we trying to do? Or rather, what should we be trying to do? If this article is meant to be documentation of what's been shown elsewhere, I expect that we could find sources for some of the criteria in some of the models, but probably not all, or even most. We'd have to deal with that somehow. Not really something to discuss in this part of the talk page, anyway.

Innate Approval Threshold: Voter behavior looks the same as dichotomous preferences, but you get different results for some criteria. Approval fails Condorcet under this model, for example, because it's suddenly possible for voters to have preferences which aren't being expressed. It's basically just meant to justify an arbitrary approval threshold the same way arbitrary preferences are justified.

Innate threshold is presumably dictatorial to the same extent that zero-strategy is; I didn't mean to suggest that it would help us deal with that problem. Sincerity just means no expression of false preferences. A>B can't be expressed as B>A, in other words. Given a model containing all possible sincere voters, approval fails IIA as we've been defining it, since there's nothing to keep them consistent. Innate threshold is basically the same as the set of sincere voters who will never change their mind about who they approve or disapprove, which allows for IIA compliance.

Proposal: My position is that we should replace zero-strategy (that was supposed to be the defining feature; every model is sincere) with an innate approval threshold preference model. It's presumably what people are talking about when they say that approval voting satisfies IIA, and it's less ambiguous than zero-strategy, in my mind. I'm hoping that's acceptable, but if not, maybe put question marks for compliance with contested criteria until it's resolved? Douglas Cantrell (talk) 06:10, 12 January 2014 (UTC)

-Arrow's work is relevant because it assumes voters have preferences, and so is universally applicable. I think relevance becomes an issue when we consider special case models such as dichotomous preferences, or innate cutoff (if it can be defined – my hypothesis is not).
-Suggest we try to reach agreement or find sources.
-Innate Threshold within Cardinal Preferences Indefinable:
An innate threshold requires a dichotomous (binary) criterion ‘D’ for the voter (i.e. not satisfied to any degree, since an alternative is either above or below the threshold). This is the model of dichotomous preferences, unless we assume the voter simultaneously has cardinal criterion ‘C’. Are 'D' and 'C' disjoint or overlapping? If they are disjoint, why does the voter use one criterion and not the other? If they are not disjoint, then it is impossible for the voter to use 'D' without ever using 'C' because they share some common meaning to the voter.
Q: Can we come up with a real-world example of “innate” voter preference whereby we can assume a voter does not exercise the expression of criterion 'C' under any circumstances? How can we assume in the model that criteria 'C' will never be used by the voter? Is 'C' meaningless or meaningful to the voter? If meaningful, what force causes the voter to never employ the criterion? If we have no explanation in the model, is the model complete, or undefined?
-Sincere is unspecified. Innate seems indefinable (outside of dichotomous preferences). I do not believe a zero-strategy voter model exists for approval (unless we change our conceptual model of the voter to dichotomous preferences, upon presenting the voter with an approval ballot.)
-In my opinion the error made in assuming IIA compliance, is that we first imagine a scenario where a voter has a discernible acceptability threshold, which is reasonable and I can essentially agree. But, to be clear, the error is the assumption that a meaningful threshold in a particular context will necessarily persist meaningfully for any available alternatives, which we have no basis to assume as along as the voter's cardinal preferences are meaningful (as explained above "HOW DO WE DEFINE 'SINCERE' VOTING?"). The only possible way to ensure IIA compliance is if the voter's cardinal preferences are meaningless, which once again proves we are adopting a dichotomous preference model.
Filingpro (talk) 05:02, 14 January 2014 (UTC)

Dictatorship: Applicability is not sufficient to show relevance. Arrow chose the definition he did because it helped him establish a scope for his impossibility theorem, which very deliberately did not address cardinal voting systems. What is the purpose of applying the definition so far outside of its intended context? To show that a subset of possible voters in the model are, by the nature of the model itself, forced to vote in a way which is indistinguishable from abstention? Do you really think that's what people would take away from a version of the table where approval is said to be dictatorial under the zero-strategy model?

Innate Threshold: Every voter has one set of ordinal preferences and one set of dichotomous preferences. Only the ordinal preferences are used when testing the voting system for compliance with criteria. Only the dichotomous preferences are used when voting. Every possible set of ordinal preferences is held by a subset of the voters in the model. Every possible set of dichotomous preferences is held by a subset of the voters in the model. Not every possible combination of ordinal and dichotomous preferences exists within the model, because every voter who simultaneously holds the ordinal preference A>B and the dichotomous preference B>A is excluded from the model. 'Ordinal' can be replaced with 'cardinal' if you prefer. Does that answer your questions?

To save time in case it doesn't, another perspective: Each voter has a cardinal preference in the range [0,1] for each candidate, and an additional cardinal value t, with all candidates valued above t being approved, and all others being disapproved. Or just say that each voter has a cardinal preference in the range [0,1] for each candidate, with all candidates valued above 1/2 being approved, and all others disapproved. Shouldn't make a difference in this context; all possible sets of cardinal preferences are included in the model.

Re - Q: I can't exactly come up with a real-world example of a preference that won't be expressed even if a malevolent god threatens the world with one million years of darkness. I do tend to think that people innately disapprove of their own death, even if they have preferences between the various options. Regardless, the model isn't meant to be realistic, it's meant to demonstrate the behavior of the system when ballots aren't being altered by external forces. Anything that doesn't imply a contradiction can be modeled. Cardinal preferences given an innate threshold can be seen as having infinitesimal meaning if that helps. The model is unambiguous; it can hardly be called undefined. I don't know what it means for a model to be complete in this context.

I assume you mean that the zero-strategy model is unspecified? Innate threshold is just dichotomous preferences with (perhaps infinitesimal) cardinal preferences serving to distinguish between candidates who are otherwise ranked equally, which is useful only in that it allows a single approval ballot and a single (full) preferential ballot to be derived from the same preference set. What was wrong with the last definition I gave for sincere voting? Innate threshold is not equivalent to dichotomous preferences in terms of compliance with certain criteria. The Condorcet criterion is a good example. Douglas Cantrell (talk) 10:00, 15 January 2014 (UTC)

Arrow applies to cardinal voter models because they are a subset of ordinals. (Any voter's cardinal preference has corresponding ordinal preferences. Ex: A:56, B:41, C:1 => A>B>C)

A rating ballot, e.g. Approval, does not change the voter model.

My question is not the Innate model, but its existential justification and/or relevance. If the cardinal preferences are meaningful to the voter, then IIA is not satisfied. If not, then the model is dichotomous preferences, because it is the only meaningful preference. If the meaning of the cutoff is derived from the meaning of the cardinal preference then we cannot assume the voter’s cardinal preferences are not used when voting because they share the same meaning to the voter.

Since we cannot come up with any example of the proposed “innate” model, this corroborates the reasoning it does not exist. My objection is including a model that does not exist and/or has no practical example we can imagine.

Of course, I yield to citations even if I think they are incorrect.
Filingpro (talk) 05:45, 16 January 2014 (UTC)

If the above is not clear, here are my concerns specifically with the recent post:

“I can't exactly come up with a real-world example of a preference that won't be expressed”
What is the relevance of a mathematical model we can imagine no example?

“I do tend to think that people innately disapprove of their own death, even if they have preferences between the various options.”
Again, I agree that voters may have a discernible acceptability threshold when faced with a set of options in a given scenario, but we have no basis to assume the acceptability threshold does not change with a different set of options. For example, when faced with a number of options that do not include death, my acceptability threshold changes. The only way it does not change is if we assume I have no other meaningful criteria other than binary life or death, which is a dichotomous preference model.

“Regardless, the model isn't meant to be realistic”.
Why are we including it?

“Only the ordinal preferences are used when testing the voting system for compliance with criteria. Only the dichotomous preferences are used when voting.”
On what basis do we assume the voter does not use preferences when voting? One example?
Any preference irrelevant to the voter is irrelevant to compliance with criteria.

Dictatorship occurs if a voter can not express a relevant preference under any circumstances.

Example why Arrow matters: If in circumstance 'A' I approve life over death, it doesn't necessarily follow that in circumstance 'B' another voter's perverse pleasure has arbitrary power over my well-being.

To answer Q’ re: dictatorship: The violation of Arrow's non-dictatorship is relevant because it reveals the lack of viability in the proposed “innate” model, not visa-versa. This is why I propose we remove the model. I don’t think it teaches the reader how Approval voting works, because Approval voting is not dictatorial. If the model is relevant then why can we not come up with one example?
Filingpro (talk) 05:45, 16 January 2014 (UTC)

RE: GOAL OF NON-STRATEGIC APPROVAL VOTING MODEL
If we define "non-strategic" to mean voting without consideration for how and whether others vote:

1. Local Innate Threshold - perhaps we could assume the voter has a meaningful dominant dichotomous criteria for a given set of options.
2. Average/Median Utility (Among Options) - raises the question what is the optimal strategy with zero information? Is there a derivable mathematical answer assuming a voter has cardinal preferences?
   

If we define "non-strategic" to mean IIA compliant, a model does not exist without a global dichotomous preference voter model.
Filingpro (talk) 23:47, 16 January 2014 (UTC)

So far, innate threshold is the only model proposed which allows approval voting to satisfy the criteria which it is said to satisfy by every other source that I've ever seen. That's the justification. I'm not going to support any edit which would cause this article to deviate further from the common understanding. Frankly I'm more convinced than ever that modelling voters at all was a mistake in this context.

We don't need to assume that voters won't use cardinal preferences when voting, because nothing short of a logical contradiction would stop us from defining the model specifically to make that a certainty, and you have not shown a logical contradiction in the proposed model.

On what grounds do you claim that preferences can't be relevant to criteria unless used by the voters? I don't recall seeing that limitation in the definition of any criteria, and even if it did exist, you could simply redefine approval voting such that it collects complete ordinal preferences from the voters without ever using most of them, much like plurality.

Your definition for Dictatorship is unreasonable. When Arrow defined it, he did so such that any failing system among those being considered would only ever use the preference of a single voter. Even if I accepted your definition, causing failure of a criterion named Dictatorship doesn't make a model dictatorial. You've only convinced me that the criterion might be poorly named.

Re: Local Innate Threshold: If that's acceptable for a given set, why would it not be acceptable for any given set?

Re: Zero Info: Optimal strategy is to vote above average utility, so far as I know, though the article also mentioned vote above median. Both strategies cause IIA failure.

Re: IIA compliance: I'm not convinced that's true, even if it's valid to call innate threshold a dichotomous preference model. Also not convinced that it isn't, mind you.

As an aside, we're going to look very silly if the accepted generalization of IIA for cardinal systems ends up being more along the lines of what I described in 2011. Also, if you really want me to address one of the points I skipped, then I will, but this discussion is getting a bit ridiculous. Would be nice if somebody more knowledgeable about the subject jumped in and explained why we're both clueless. Douglas Cantrell (talk) 08:44, 17 January 2014 (UTC)

ACTION SUMMARY: I believe the best option is to remove the model we can not agree on until a source for the model and determination is found. Please feel free to add citations.
I agree to disagree on the following:
FALSE: We are allowed to assume a voter has meaningful preferences the voter will never use when voting.
-The contradiction occurs because if the preferences are meaningful to the voter, there is no basis to assume the voter will never use them. Just because we say so doesn't remove the contradiction.
FALSE: The ballot determines the model for the criterion.
-If this were true then the model of Approval is dichotomous preferences and it passes every voting criterion and is the perfect voting system, but it isn't.
FALSE: An approval voting model's failure of Arrow's non-dictatorship is irrelevant.
-Because Arrow only assumes voters have preferences, violating non-dictatorship is of critical importance. (My "Dictatorship" statement above in bold was not a definition but a condition that can cause dictatorship.)
Re: "Common/Traditional Understanding" Citations? Sources? Hearsay is not a Wiki standard. In my opinion, any source that says Approval passes IIA is not credible or will be overturned. The method allows voting for any number of available candidates.
Re: Marking ordinal preferences on an approval ballot: yes we agree that is exactly why voter preferences are correctly used in the criteria compliance, but the error is assuming a voter preferring A>B can never approve A under any circumstances.
Re: Q "Local Innate Threshold" means life or death criterion may be innate in one scenario, but in another scenario of torture vs no torture I can vote for 'no torture' only - i.e. the innate threshold is local to the available options. In "[Global] Innate Threshold" (which I am certain does not exist or it is dichotomous preferences), I must approve both torture and no torture if my dichotomous preference is life or death. That is how they are different.
-I find the discussion has been illuminating, and to end it one compromise might be to set up a separate section or paragraph for "Approval and IIA" as a forum for "traditional" compliance and cite the sources alluded to (despite my objection), and perhaps contradictory findings by published authors. Meanwhile, this table could stand on its own as "rational voter model" with different cutoffs considered that we all agree to - i.e. rational as in assuming voters can possibly vote in accordance to advance their preferences.
-The current posting is unacceptable because:

1. "Sincere" as defined in the article is an unspecified cutoff therefore we have no basis to assume it can not change with available candidates.
2. The footnote for IIA has no basis (to arbitrarily assume an inherent cutoff when one does not exist, and assume a voter will never vote in accordance with their own preferences). The footnote also has no citation, and I am requesting the determination or model be removed. I would put "No" for IIA with footnote "Any sincere cutoff may be chosen by the voter in accordance with the voter's ordinal preferences in a manner entirely at the discretion of the voter, and therefore may vary with available alternatives." Who is correct? We need a citation since we can not persuade each other.

Filingpro (talk) 05:37, 18 January 2014 (UTC)

PROPOSAL:

• Non-dictatorship (REMOVE)

• Unrestricted domain (ADD) — A voter may have any preference ordering of the alternatives.

Rational voters		Unrestricted domain	Pareto efficiency	Majority	Monotone	Consistency & Participation	Condorcet	Condorcet loser	IIA	Clone independence	Reversal symmetry
Cardinal preferences	Zero information	Yes	No	No	Yes	Yes	No	No	No	No	Yes
	Imperfect information, strategy	Yes	No	No	Yes	Yes	No	No	No	No	Yes
	Strong Nash equilibrium (Perfect information, perfect strategy)	Yes	Yes	Yes	Yes	No	Yes	No	No	Yes	Yes
Dichotomous preferences		No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes

REASONING:

simpler, clearer, and satisfies the request for both strategy-free and IIA compliant models, while avoiding models and determinations we can not agree on and have no citation

Filingpro (talk) 05:37, 18 January 2014 (UTC)

Approval Failure IIA Obvious NOT WP:SYNTH: Can it be agreed on that in practice Approval does not pass IIA? We need only consider the simple possibility that a voter might plurality vote. Shouldn't this constitute not WIKI SYNTH on the grounds that it is obvious?
Filingpro (talk) 21:30, 18 January 2014 (UTC)

Recent Posting (different than chart above - see article):

-I included an irrational voter model to replace "sincere" because every model is sincere.
-I lowered the irrational model because it is a special case.
-I used neutral technical language to describe the "absolute dichotomous cutoff" within the cardinal preferences of the voter. We don't know the cutoff is "innate" if the voter only has only cardinal preferences and is merely calibrating their absolute cardinal scale to the available ratings "approved", "not approved".
-I removed "perfect strategy" from zero information model because this accounts for a voter who has unbound cardinal preferences and no inherent dichotomous cutoff, and has no intent to game the election (by predicting how other will vote) but merely vote rationally.
-The restricted domain of dichotomous preferences is important to disclose - helps the reader understand what the voter model means.
Filingpro (talk) 21:19, 19 January 2014 (UTC)

@Douglas Cantrell: To the goal of "innate" I suggest adding a lower row model "Expressive Absolute Scale" satisfying IIA and with NA for non-dictatorship because we assume the voter's rational goal of using sincere cardinal preferences to make a choice amongst alternatives on the ballot is secondary to the expression of each alternatives's performance on the absolute scale. An example would be a voter in party A who when voting for only two candidates in the opposing party B, and where the voter has strong preferences for one, the voter still votes for neither (casts an empty ballot) for the purpose of expressing disapproval of both. This model assumes the voter has motives external to the outcome of the election itself.
Filingpro (talk) 03:53, 20 January 2014 (UTC)

Lots of comments to respond to. Starting from the beginning:

Modeling voters such that they have preferences which aren't 'meaningful' does not imply a logical contradiction. You don't need any basis to assume something about a model which you're defining yourself; any assumption you make is part of the model, and thus true with absolute certainty. You haven't shown a logical contradiction in the model, you've only explained why it probably isn't realistic.

I don't know what it means to say that the ballot determines the model for the criterion, but I'm pretty sure I never said it.

You've only shown that Arrow's non-dictatorship is applicable, not that it's relevant. I could create a new criterion called Bucklin-Equivalence which makes the same assumptions as Arrow's non-dictatorship, while only being satisfied by Bucklin voting. It would be applicable in many places, relevant in none. Your condition for causing Dictatorship is still impossible in the context where the criterion was defined.

I'll address sources at the bottom of my response. How is the ability to vote for any number of candidates relevant to IIA?

Your response to marking ordinal preferences on an approval ballot doesn't seem relevant to my point. You've been saying that voters never express their ordinal preferences in the innate threshold model. I'm saying that you can just as easily imagine that they do, and that the voting system ignores them, like in plurality.

Different sections for criteria compliance with and without voter modelling is something which I would consider acceptable, but I expect that would take significant time to do properly, or at least more than I have at the moment. Also, I wasn't trying to end the discussion, I was trying to trim branches which didn't seem productive.

In practice approval voting does not satisfy IIA, but in practice there's no such thing as a Condorcet compliant voting system. What happens in practice isn't really relevant to compliance with voting system criteria.

I have no idea why absolute dichotomous cutoff would be acceptable when innate approval threshold isn't, but I'm not going to complain. They are, in my mind, completely equivalent.

I don't understand why you removed 'perfect strategy' from the zero-info model; perfect strategy given zero-info is to approve above average utility. That's also rational behavior. How are unbounded preferences, inherent cutoffs, or predictions relevant to this change? I wouldn't really care, but now there's an inconsistency between the descriptions for zero information and imperfect information.

I really don't want to go through the same mess as non-dictatorship trying to understand unrestricted domain in this context, so I'd very much appreciate a source which discusses that criterion in the context of approval voting if you can find one.

Re: Sources - Finding sources on this subject is a nightmare, and finding ones which are free is even more so. Interpreting them isn't exactly trivial either, at least from my perspective. Best source I've been able to find so far is here. Note that I haven't had time to read all of it yet, and I didn't necessarily understand all that I read. Douglas Cantrell (talk) 09:13, 22 January 2014 (UTC)

I think our discussions have greatly improved the article. I am open to improvements. Quick comments and I will post again other topics…

---

I essentially agree with you we are allowed to postulate the absolute dichotomous preference within cardinal preference (despite my objections to relevance), and have included it.

---

Here is an example of why failure of non-dictatorship is relevant:
Voter A Criteria: Environmental Preservation, Scale 0 – 100, absolute cutoff = 50
0 = complete environmental destruction
100 = complete environmental preservation

Voter B Criteria: Hunting Homeless People, Scale 0 – 100, absolute cutoff = 50
0 = cannot hunt homeless people
100 = full access to hunting homeless people

TWO Options X, Y
Voter A Preferences: X:100, Y:50.00…001, “approves” XY
Voter B Preferences: Y:50.00…01, X:49.99… “approves” Y

Result: ‘Y’ is winner so 50% of the environment is completely destroyed, arbitrarily. Why? Because there are no objective criteria used by the voters, the position of each alternative relative to the absolute cutoff and the relative strength of preference between the voters’ ballot markings is completely arbitrary. Note that voter A has a very strong preference between A and B, and voter B is nearly indifferent. For voter A 50% of the environment is at stake. For voter B there is a barely perceptible increase in the access to hunting homeless people.

Now suppose option Y causes slightly more environmental destruction, and X slightly more access to hunting homeless people:
Voter A Preferences: X:100, Y:49.99…, “approves” X
Voter B Preferences: Y:50.00…01, X:50.00…01 “approves” YX

When one of the options causes an arbitrarily smaller amount of environmental destruction, the result is that 100% of the environment is now preserved rather than 50% being destroyed!

We can also think of voter A preferences for X and Y oscillating with maximal differentiation above the cutoff. Think of voter B’s preferences oscillating around either side of the cutoff, with near indifference.

In a democracy, voter A’s environmental interest is given equal weight to voter B’s recreational interest.

Approval voting is democratic, because voters can “vote for any number” of available alternatives by using their sincere preferences, without any strategic information about other voters or consideration for how others might vote. The voting system does not intrinsically enforce an immovable cutoff on an absolute scale. Of course "vote for any number" means voters can "vote for one", because one is any number.

Filingpro (talk) 05:23, 24 January 2014 (UTC)

I'm going to be responding to these posts individually for sanity's sake, but it's just going to make things worse if you don't start indenting your responses. Place one " : " at the beginning of each paragraph for every level of indentation desired. Or you could just put everything at the end of the section, if you prefer. So long as everything at a given level of indentation is in chronological order, things should stay manageable.

As for my actual response: Would it be a fair summary of your point to say that the model allows voters with strong preferences to abstain even when those with weak preferences do not, and that Arrow's Non-Dictatorship criterion should be included in the table so as to communicate this to readers? If so, my response would be that the criterion wasn't defined (or named) with that purpose in mind, and that including it can't really be expected to do anything of the kind.

The point is if V1:A>B and V2:B<A then V2 should not decide arbitrarily. V1 should not be disenfranchised merely for holding certain opinions or values. Does that make sense? Does that also answer your relevance question? Filingpro (talk) 22:41, 26 January 2014 (UTC)

It makes sense, but saying that something shouldn't happen is different from saying that we should make note of it when it does by calling the relevant model dictatorial. I'm only contesting the latter point. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

The example you gave really isn't that shocking, by the way. Democracy says two wolves get to kill one sheep even when there's a dead cow nearby. Likewise, a preference for beef can make the difference between life and death. It's odd that the sheep would abstain, but the model is meant to show what approval voting does with the information it actually has, not to predict the results of a real election. Douglas Cantrell (talk) 10:13, 25 January 2014 (UTC)

Separate issues: (1) constitutional protection of minorities (2) democratic group decision. Agreed? Filingpro (talk) 22:41, 26 January 2014 (UTC)

Definitely separate issues. I was just commenting on the connotations of your argument, not its meaning. If the connotations weren't important, then neither is this thread. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

Yes I agree easier for us and the reader to have one compliance table rather than separate section.

Apologies for mis-quote. It makes sense to me that cardinal preferences is a universal voter model that doesn't change merely when voters are presented with different ballots – perhaps we are in agreement.

RE: “In practice approval voting does not satisfy IIA, but in practice there's no such thing as a Condorcet compliant voting system. What happens in practice isn't really relevant to compliance with voting system criteria.”

I assume the argument here is that “non-strategic” Approval passes IIA? Condorcet compliant voting systems never satisfy Condorcet because voters use strategy? The problem is that Approval voting fails IIA when voters apply their sincere cardinal preferences, without information or consideration for how others might vote. Condorcet compliant systems satisfy Condorcet criterion under the same conditions.

Perhaps we need not debate this since all the models are presented now in the table.

Unrestricted Domain - this is pretty straightforward - Arrow's Nobel prize theorem is undisputed. The only way to get around the theorem is assume voters don't have preferences. There is no such thing as a perfect voting system. I think this is very instructive to the reader and the determination is obvious. I think its very important that we see how different models for Approval violate various conditions of Arrow's theorem since his work is so crucial to the understanding of the single-winner voting problem.

Zero-info without "perfect strategy" - it seems any arbitrary rational strategy has the same compliance so the text is redundant. In other words I don't think we need to add the specificity unless its meaningful, while the generality of the table row I believe is important because it gives a row in the table for myself to vote if I don't know about how other vote, and I don't know what the perfect strategy is. I think it helps the reader generally understand how Approval voting might perform when rational voters use it without information about how others will vote. Perfect strategy is not required.

Filingpro (talk) 07:23, 24 January 2014 (UTC)

I wasn't trying to make any particular point about IIA compliance and Condorcet compliance being equivalent, I was just saying that real elections aren't relevant to the criteria being discussed, because real voters don't conform to any sane model. They aren't even consistently sincere.

I wasn't questioning the relevance of Unrestricted Domain, I was trying to figure out what compliance even means in this context. That said, you're seriously overstating the applicability of Arrow's Theorem. The theorem simply doesn't apply to approval voting, or any other non-preferential voting system.

Can we let the reader decide the importance of Arrow? Arrow applies to Approval because he only assumes voters have preferences. Arrow's voter model and ballots are unified. His work is a proof of impossibility for any aggregation rule on voter preferences. For Approval we need only consider how voter preferences are applied to the ballot. Failing unrestricted domain means we change the assumption that voters have preferences - i.e. we restrict voters to only having certain preferences. We are clearly not saying Approval trivially fails unrestricted domain as alluded to in the link, because most of the models we show do not restrict the domain, and pass; however, we have an obligation to show when the domain is restricted by a particular model, because this is an axiomatic assumption in voting, that voters may have preferences among alternatives. Lastly, claiming Arrow doesn’t apply to Approval is an obvious contradiction if we have IIA in the table. If we have IIA in the table, we must show failures of unrestricted domain, dictatorship, Pareto etc. because they are all from the same theorem. IIA can not apply if Unrestricted Domain does not apply. Filingpro (talk) 22:41, 26 January 2014 (UTC)

It's not a question of importance, it's a question of whether or not Arrow's theorem even applies. No sense in debating the point if there's a citation available, so here's one from Arrow himself:

"Now there’s another possible way of thinking about it, which is not included in my theorem. But we have some idea how strongly people feel. In other words, you might do something like saying each voter does not just give a ranking. But says, this is good. And this is not good."

That said, his theorem can be generalized, and I don't have any objection to applying the generalizations, given proper citations. As for Unrestricted Domain, my interpretation is that dichotomous preferences is one of the only models that IS compliant, but I really don't want to have that argument, which is why I'm hoping you'll find some sources.

I'm pretty sure Arrow didn't invent the IIA criterion, but even if he did, there's no reason we'd need to include other criteria from the same theorem. I realize that isn't much of an argument, but I'm not sure I even understand your logic there. Is it a question of notability? Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

I'm only complaining about the inconsistency. If perfect strategy isn't used to describe zero info, it shouldn't be used to describe imperfect info either. Douglas Cantrell (talk) 10:13, 25 January 2014 (UTC)

Yes. I also had considered that "perfect" strategy is not needed when the information is already imperfect, and is also unnecessarily specific. Therefore, I removed "perfect", for editorial consistency and broader application of the models. Filingpro (talk) 22:41, 26 January 2014 (UTC)

But now we have 'strategy' in the description, which is both undefined and potentially misleading if understood to mean 'insincere.' Why not just say that voters are rational, and leave it at that? Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

RE: strategy and the CENTRAL PROBLEM WITH IIA COMPLIANCE FOR APPROVAL: In Plurality Voting "vote for one" given two candidates, we never say a voter who prefers A>B is voting strategically when voting for 'A'. In "vote for any number" why would we say a voter is voting strategically when voting for 'A' just because they do not suddenly abstain? Why would changing the ballot from "vote for one" to "vote for any number" cause a voter to abstain? Why in one condition voting for the preferred candidate is not strategic, and now simply because the voter is allowed to vote for more than one option the voter must abstain to be non strategic? I very much would like to know why this is not absurd. I don't think IIA failure by Approval is even WP:SYNTH because everybody knows voters can vote for at least their most preferred option in a democracy. This is obvious.
Filingpro (talk) —Preceding undated comment added 07:47, 24 January 2014 (UTC)

Edit: Pretty sure I misunderstood what you were responding to; disregard the next paragraph. None of my arguments are based on labeling something strategic behavior. That was a misunderstanding. As for IIA, it depends on the voter model, and I don't think there's any question that the dichotomous cutoff model satisfies IIA. I think the argument over whether or not the model should be included is also pretty much resolved for the time being, isn't it?

Thanks for clarifying. Yes. I agree to including it (as a compromise despite my objections on grounds of relevance), assuming we include all Arrow criteria IIA and non-dictatorship & Pareto, that distinguish models shown in the table. Filingpro (talk) 22:41, 26 January 2014 (UTC)

(One technique I have used in the past when retracting a paragraph is strike-through, rather than removing it.) Filingpro (talk) 02:19, 27 January 2014 (UTC)

Including the model was meant to be conditional? I'd thought that finding a source would be sufficient. I have concerns about including those criteria without citations, but that's something to discuss in other threads. I would've used strike-through, but I wasn't sure how that works on this site. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

If your reference to plurality was derived from my own, then you seem to be misunderstanding my point. Plurality can be understood as accepting ballots of the form {A>B>C>D}. Plurality only ever uses the first '>'. Approval voting can be understood as accepting ballots of the form {A>B>C>D, n}. Approval voting only ever uses the nth '>'. You objected to the fact that voters had preferences which weren't being expressed, so I gave them a mechanism by which they could express those preferences, with plurality serving as precedent for ignoring them. I don't know why you're talking about strategy; that's handled by the voter models. Douglas Cantrell (talk) 10:37, 25 January 2014 (UTC)

RE: sources - agreed I hope to be able to do some more library research in coming months

RE: The doc linked to above, by Remsi Sanver, the model...

"We assume two cardinal qualifications, "good" and "bad", with a common meaning among individuals. This can be interpreted as the existence of a real number, say 0, whose meaning as a utility measure is common to all individuals...Henceforth, "approval" is not a strategic action but has an intrinsic meaning: It refers to those alternatives which are qualified as good." - M. Remzi Sanver

Basically the model is that we all have our own notion of good and bad and we all agree to call the middle ground 0.

Problem I: The obvious problem I see is that what happens to the voter I mentioned in the previous example? (repeated here)
Voter A Criteria: Environmental Preservation
worst case = complete environmental destruction
best case = complete environmental preservation
Q: Is only a little bit of environmental destruction "good"? What is my "zero" i.e. neutral point?

Problem II: Everyone considers pizza good (poison is bad). How do we vote on toppings? Total Pareto Efficiency Failure.
Filingpro (talk) 09:40, 24 January 2014 (UTC)

Problem I: I don't understand most of the things you wrote here. It doesn't matter where the threshold comes from so long as it's static and universal. That's why I was pushing to call it innate, just like preferences, and to actually call it a distinct preference model.

I am open to calling it "innate" if we can come up with one example. Filingpro (talk) 02:19, 27 January 2014 (UTC)

Why does there need to be an example? It's already been established that the model isn't realistic, and that there's no particular reason it needs to be. We're not trying to explain something which exists, we're trying to describe something useful which can be imagined. Calling the threshold innate serves that end. Leaving it ambiguous does not.

Also, you seem to be taking it as a given that people are consequentialist. I'm not about to contest that assumption, but it's something to be aware of. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

Problem II: You'd vote as normal, and every non-poison candidate would tie, since you deliberately excluded anyone with a useful threshold from the election. Pareto efficiency is failed to precisely the same extent it's failed in any other model, i.e. only in a very trivial sense. Douglas Cantrell (talk) 10:15, 25 January 2014 (UTC)

1. The voters excluded, in an election between (1) poison and (2) pizza with a less than desirable topping, abstain, even if they know they are the only one voting. I would like to know why this assumption is not absurd.
2. Failure of Pareto Efficiency is not trivial when it is guaranteed failure, not just possible failure, in common real life situations. Members of Party A have an absolute cutoff such that they vote for members of their own party and not for members of the opposition party B. Therefore, party A members are incapable of distinguishing any candidates in their own primary because every voter approves every candidate from their own party. Similarly, even Brams, Approval guru, suggests how Approval can be used to narrow the field in a runoff election (source provided upon request). But what if a voter has disapproved three candidates in the first election that are now the only three options in the runoff? Is this voter not permitted to vote in the final election despite having meaningful preferences? Absurd, useless assumption! Likewise, most people don't consider pizza bad on an absolute scale with poison, homicide, torture, starvation etc. People do vote for toppings in real life. The assumption that voters can never choose among several 'good' options when they have meaningful preferences is indeed absurd. I do not see how this position is defensible. Of course, voters calibrate a new cutoff based on sincere preferences in the context of pizza, not Chinese Food, or Italian etc. Filingpro (talk) 22:41, 26 January 2014 (UTC)

It isn't absurd because there are any number of other examples which rely on the same assumption that give useful insight into the nature of the voting system.

Real life elections and primaries are irrelevant to the question of whether or not a given voter model causes Pareto efficiency failure. If you have a formal example of non-trivial failure given a sincere voter model, I'd love to see it.

To say that innate threshold is the only model with value might be indefensible. That isn't something I ever said. If you want to model a typical election for toppings, innate threshold isn't the best choice. If you want to communicate that approval voting is internally consistent while acknowledging that it won't necessarily elect the Condorcet winner when voters have cardinal preferences, innate threshold is the only suitable model yet proposed. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

Example Approval Failure Of Common Spoilers (Failure To Resolve A Vote Split): Shows failure of IIA and Condorcet with sincere voting based on the options available (e.g. average utility – i.e. voters pick a logical midpoint with no intent to game the election, but merely express their sincere preferences) L = liberal, politically left R = conservative, politically right RC = right center LC = left center*

Imagine the classic “spoiler” problem with two strong candidates from either party fighting over the center, RC and LC. The liberals have a majority of 52% (often called a clear win or “mandate”). But a spoiler enters the race on the far left, L:

• NOTE ADDED: The example below assumes voters can have at least partially multi-dimensional criteria - i.e. liberals have criteria for national security, economy, environment, democratic reform, social issues, welfare etc...IMPORTANT: see diagram below "EXAMPLE NON-STRATEGIC APPROVAL FAILURE IIA DUE TO COMMON VOTE-SPLITS" Filingpro (talk) 23:57, 24 January 2014 (UTC)

(Voter approvals in bold)

Simple example…
48: RC
5: LC (left center voters that don’t like extreme left or right candidates)
42: LC, L
5: L (purist left voter utilities = L:100, LC:45, RC:0)
RC wins. Remove ‘L’ from the election and LC wins.

More detailed example…
40: RC:100, LC:45, L:0 (conservatives most prefer their right center candidate, and vote against left candidates)
8: RC:100, LC:55, L:0 (independent near center conservatives strongly oppose the far left candidate L)
4: LC:100, RC:55, L:0 (independent near center liberals are closer to the center right than the far left)
4: LC:100, L:45, RC:0 (left center voters that don’t like far left or right candidates)
16:LC:100, L:75, RC:0 (left center voters that vote all left)
18:L:100, LC:75, RC:0 (far left voters that vote all left)
10:L:100, LC:45, RC:0 (purist left voters see the left-center as mostly contrary to their values, and the right candidate a stronger betrayal)

Approvals:
RC = 52, winner by spoiler L
LC = 50
L = 44
RC wins. Remove ‘L’ from the election and LC wins.

There are several natural variations of this example that can fail the criteria mentioned.
Filingpro (talk) 16:35, 24 January 2014 (UTC)

Your first example doesn't have enough information to demonstrate relevance to a rational voter model.

The 5 voters in the first example, preferring L:100, LC:45, RC:0, voting rationally when L is removed from the race will approve LC, changing the winner from RC to LC, failing IIA. Filingpro (talk) 22:41, 26 January 2014 (UTC)

Your second example is interesting. Approval voting normally favors centrists, so it's weird to see LC losing because of a candidate further left than themselves, to the point that I thought I'd find a mistake in your math. Really wish I could see the actual positions of the voters and candidates in issue space, supposing it's even possible to get those numbers with fewer than four dimensions.

Anyway, why'd you bring this up? IIA and Condorcet failure in the zero-info model wasn't being contested. Douglas Cantrell (talk) 10:13, 25 January 2014 (UTC)

Please see "non-strategic question" issue below...* Filingpro (talk) 22:41, 26 January 2014 (UTC)

EXAMPLE NON-STRATEGIC APPROVAL FAILURE IIA DUE TO COMMON VOTE-SPLITS (a.k.a. "SPOILERS")
Voters vote for any number of available locations (e.g. x, y, z) based on convenience to all. Voters vote cooperatively without knowing how others might vote, and so they approve only locations closer than average distance among the available options. We might instead suppose there is an objective judge that measures the distance of each voter to the available locations, and to ensure fairness approves for each voter any location closer than the average distance. In this way we ensure there is no possibility of strategic voting.

There are 3 voters at location A.
There are 2 voters at location B.
There are 2 voters at location C.

+++++++++++++++

+++++++++++++++

++++++++++++C++

+++++++++++++++

+++++++++++++z+

+A+++++++++++++

+++++++++++++++

++x++++++++++++

+++++++++++++++

+++++++++B+++++

+++++++++++y+++

+++++++++++++++

+++++++++++++++

+++++++++++++++

+++++++++++++++

Race x vs y
3 A Voters (x:2.27, y:11.18), approve x
2 B Voters (y:2.27, x:7.28), approve y
2 C Voters (y:8.06, x:11.18), approve y

y wins

Add irrelevant alternative z...

Race x vs y vs z
3 A Voters (x:2.27, y:11.18, z:12.04), approve x
2 B Voters (y:2.27, z:6.71, x:7.28), approve y
2 C Voters (z:2.27, y:8.06, x:11.18), approve z

x wins (adding z changes the winner from y to x!)
Filingpro (talk) 23:50, 24 January 2014 (UTC)

None of the voters did anything that they wouldn't do if they were using optimal strategy given zero information. What difference does it make whether or not they were being strategic, by any given definition?

• The example categorically rebuts the claim that IIA failures by Approval are strategic and not valid. We can see in this example we can pick any logical, consistent midpoint by an objective judge as to the actual distance for each voter to the available locations, and we fail IIA. I'm quite sure that even if we make approval cutoffs less strict for each voter proportionally (to approve locations further away), we can still show IIA failure by adjusting the example. If the entire domain of logical midpoints all fail IIA, it is impossible to say that IIA failure is the result of strategy. Filingpro (talk) 02:19, 27 January 2014 (UTC)

Did I attribute IIA failure to strategy at some point? I don't recall doing so. I may have attributed it to external forces, i.e. any mechanism by which cardinal preferences are translated into approval ballots, including the one you just described. Granted, that's also how I define strategic voting in the context of approval voting, but that just means you haven't eliminated strategy as I happen to define it. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

That said, nice to see a proper model of an election with IIA failure that doesn't favor a centrist, so thanks for that. I wonder what kind of conditions make that possible... Douglas Cantrell (talk) 10:13, 25 January 2014 (UTC)

Agreed. The example illustrates that Approval voting fails to resolve common vote-splits reliably, and does not satisfy IIA.Filingpro (talk) 22:41, 26 January 2014 (UTC)

That's a peculiar way to phrase it. It's normally advantageous to have a similar, but more extreme candidate run in the race with you, because it makes you look better to moderates. Moderates are a lot more numerous in reality than the voters who are clueless enough to think that bullet voting for the extremist makes sense in that scenario, which is why approval voting has a centrist bias. Behavior which isn't consistent with that bias is hardly common.Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

Specifically, consider an evangelical conservative voter, who strongly opposes gay marriage and abortion, who votes for the right-center candidate in a head-to-head race against the left-center, while both candidates are pro-choice and do not oppose gay marriage. An evangelical conservative candidate (anti-abortion, anti-gay) can spoil the election upon entering the race, because to the evangelical voter this is the only candidate that matches their views closely, such that the two center candidates become more alike (i.e. below average utility based on available options). Filingpro (talk) 16:53, 27 January 2014 (UTC)

I added comments above in multi-threaded form. Probably ok with two of us. Another possibility is using '#' to number points, or start new sections for main topics - e.g. "unrestricted domain" etc. Thanks Filingpro (talk) 22:41, 26 January 2014 (UTC)
Started new sections for each topic below... Filingpro (talk) 04:18, 27 January 2014 (UTC)

Unfortunately I didn't see this until I'd already written my responses, so migrating to the new sections will be delayed a bit. Still, thanks for making them; this section has become a bit of a mess. Douglas Cantrell (talk) 07:40, 30 January 2014 (UTC)

Thanks I read all recent comments above. Yes how about we move to new sections for any issues by subtopic at this point?

You say the innate model you propose "isn't realistic" and "Real life elections and primaries are irrelevant".

An absolute cutoff model is included in the article. Filingpro (talk) 22:19, 7 February 2014 (UTC)

Counting faster. Can we improve this?

Re: "Counting ballots in approval vote is faster than some other alternative voting methods, such as ordinal systems, and can be completed at the local level."

Good point re: local level and sum-able.

The problem I see is the broader assumption that approval ballots can be counted faster than other methods.

The following is more accurate, but I would like to come up with something more concise:

Counting machines can read approval ballots as they are submitted by voters, keeping only a tally of the total approvals for each candidate, without needing to store a record of each ballot as required by Instant Runoff and many other ordinal methods.

Approval voting ballots in a national election can be tallied in local precincts independently and then summed to determine the results. In contrast, distributive counting in Instant Runoff requires synchronization of local precincts with each elimination round, or publishing voter data from each local precinct for national computation.

Hand counting ballots in Approval voting is more difficult than Plurality pile counting or Instant-Runoff which uses successive Plurality rounds only as needed to reach a majority, and which only recounts the minimum number of ballots in each elimination round. Approval pile counting requires a pass on every ballot for each candidate in the election, or requires sorting ballots into 2^N piles (where N is the number of candidates), representing the possible combinations of voter approvals. For example, ten candidates would require either 1024 piles, or performing ten separate counts on all ballots. In practice verification of paper ballots may require synchronization (i.e. data entry) into a computational device such as a computer spreadsheet or software.

Perhaps the existing statement can merely be modified to reflect some of this important information, especially regarding hand-count verification. Perhaps I can return to this when I have more time... Filingpro (talk) 10:13, 29 October 2013 (UTC)

I agree on some of this but Approval pile counting sounds like nonsense. Who counts political ballots in piles? All you need is one pass through the ballots and N accumulators, identical cost as plurality. And if you're in a hurry you can just count major candidates, and count the rest as "other" and be happy as long as other stays small. Tom Ruen (talk) 21:35, 29 October 2013 (UTC)

Here are some election scenarios to consider hand-counting...

1. See the ballot for the Egyptian Primary 2012 (right):
2. A school with 10 candidates running for student council and a student body of 1000 with no voting equipment.
3. 200 people in a meeting choosing among 10 options where anonymity is required.

Is approval counting faster than IRV for the above elections?

The hand counting algorithm is a question for any democratic voting system where either voting equipment is not available or hand count verification is demanded to ensure correctness of voting equipment or detect fraud.

Simultaneous cardinal accumulators must be virtual (or symbolic) and require synchronization with paper ballots, whereas plurality pile-count accumulation is immediately visually verifiable - i.e. the tallies and the physical piles have a direct correlation.

This a categorical difference. But I would like to know more about how verification works in practice. I am open to finding sources on this so I can agree to your challenging the source.

You make a good point regarding the N accumulators and lower cost when using existing counting machines designed for Plurality. My broader point is that saying "Counting ballots in approval voting is faster" is not a scientific statement, but a subjective one, that requires clarification if we want to put it in the article. Request: How about we add something along the lines of what you put here on the talk in the article to clarify what we mean by "faster"? I think your writing is good on this.

I also agree with the implications of your point, that in practice Approval hand counting would be distributed and require a single pass on the ballots assuming administrators kept a sheet with separate tallies for each of the candidates (also as I suggested in my posting). How this affects hand counting speed and visual verification compared to pile counting (i.e. sorting ballots into physical piles) I believe is another question. — Preceding unsigned comment added by Filingpro (talk • contribs) 02:52, 31 October 2013 (UTC)

Filingpro (talk) 02:59, 31 October 2013 (UTC)

Re: your question "Who counts political ballots in piles?"...

http://www.youtube.com/watch?v=k1hBvLYOwug&t=0m49s

http://www.youtube.com/watch?v=dEUN9QezFdw&t=4m4s

http://www.youtube.com/watch?v=BLxzjyMe5H4&t=1m24s

Filingpro (talk) 06:40, 31 October 2013 (UTC)

The reason I questioned "counting ballots in piles" is that most ballots contains MANY elections, so it seems wasteful to say you have to recount and pile ballots for every election, but if you're talking about verification counts (or official recounts) on a specific close election, it can make more sense. And in an official recount that is close enough, there will be a first-count winner and challenger who is close enough to demand a recount. So in that case, you can pile ballots just like plurality, and you can have 4 piles: A, B, both, neither. Anyway, just like having 10 elections, you have 10 counts, so if you have an approval election with 10 candidates, you can make 10 counts by candidate of 2 piles approved, not. These piled counts can be done in parallel by many counters, like 10 people each can take about 10% of the ballots, doing their careful piling for their candiate they're counting, and then rotating the piles around until everyone has counts all ballots. So again, just like plurality ballots with multiple elections. Tom Ruen (talk) 07:08, 31 October 2013 (UTC)

Thanks, Tom. Yes - I agree with several of these points.

I think your points are (1) assuming machines are available, hand counts would only be for challenges (2) approvals can still be pile counted, if necessary, even for 10 candidates by distribution and rotation.

My goal is to improve the article by clarifying the statement “Counting ballots in approval voting is faster”. Is there a source for this? What is the context of the assertion from the source? Hand counting? Machine counting? Local or national elections? How much faster, milliseconds, seconds, minutes, hours, or days?

Here are some things to consider…

In your hand counting example, IRV would be faster (ambiguous at best).

Machine counting ballots in RAM is effectively the same for Approval & IRV, with respect to tallies and loop counts, both scale in the best case by order B (number of ballots), and approach B * N worst case (where N is number alternates).

Modern computing, storage, and networking provide ample random access to data, so that effectively real-time IRV results can be realized.

The public having random access to published vote files (with cryptographic hashes) is important for verification. See Ka Ping Yee doctoral thesis p.50 "practical example" read through p.51. (Yee also recommends Approval and criticizes IRV/Hare)

NOTE: I've updated the article with the intent to clarify "faster". Please feel free to edit, of course. My request is that if we say "faster" then what is the source, context, assumptions made etc? (as I explained above)

We agree that when hand counting either multiple elections or approvals, tallying would likely be used rather than pile counting. Below I will post some interesting info I found on the tallying method.

Filingpro (talk) 02:42, 4 November 2013 (UTC)

Some interesting info on hand-tallying... (for notes re: recent posting, please see above)

The links below show examples where there are at least four people tallying:

1. a counter who reads the ballots and definitively setting them aside
2. someone to check to see if #1 is doing so correctly
3. a tally person #T1
4. a redundant tally person #T2.

I assume/guess the two talliers marks are compared to ensure the recording is correct. Tallied ballots are put into boxes which are identified to correspond to the tally sheets. The tally sheets become the masters, but anyone could spot check a sheet with a corresponding box. The tally marks become the visual analogy for the counts for each candidate, and can be summed with calculators. Tally sheets can be spot checked for correct summations.

http://www.youtube.com/watch?v=e6iWInfi1RM

http://www.youtube.com/watch?v=X9eaUVU0nbM (more people observing the ballot readers and talliers)

(there are other videos that can be found)

Filingpro (talk) 03:12, 4 November 2013 (UTC)

Your article edits make sense to me, "faster than some other methods" wasn't a very useful claim. Tom Ruen (talk) 04:32, 4 November 2013 (UTC)

Us for 'Multiple winners ' is NOT subject to Burr's dilemma

Burr's dilemma only applies to single winner systems. See Burr dilemma — Preceding unsigned comment added by BWernham (talk • contribs) 09:30, 20 November 2013 (UTC)

Unrestricted Domain

Continuation from multi-threaded comments above in section Compliance Proposal Disclosing Failure of Democratic Criteria.

WHY FAILURE OF UNRESTRICTED DOMAIN IS OBVIOUS WHEN ASSUMING DICHOTOMOUS PREFERENCES
The domain is the input set to the system. Arrow’s IIA assumes the input set may include the range of all possible transitive preferences by voters for the alternatives. When we don’t allow as input to the system the full range of preferences, we obviously violate this criterion.

The relevance of its failure has already been acknowledged. Filingpro (talk) 04:16, 27 January 2014 (UTC)

The article dedicated to Unrestricted Domain calls it "a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed." I interpret this to mean that you cannot ignore any possible cardinal preference ordering if voters have cardinal preferences, that you cannot ignore any possible ordinal preference ordering if voters have ordinal preferences, and that you cannot ignore any possible dichotomous preference ordering if voters have dichotomous preferences.

If Dichotomous Preferences fails Unrestricted Domain because it 'ignores' (i.e. fails to uniquely represent) a subset of the possible ordinal preference orderings, then why would any preferential voting system comply with Unrestricted Domain, given that it ignores a subset of the possible cardinal preference orderings in precisely the same sense?

I also think that most (all?) of the other voter models fail Unrestricted Domain, because they all use 'other considerations' to translate non-dichotomous preferences into dichotomous ballots. I'm less confident about that interpretation, however.

I'm pretty sure I never said that Unrestricted Domain is relevant, by the way; I simply chose not to contest the point. Douglas Cantrell (talk) 08:07, 5 February 2014 (UTC)

The other models do not restrict the possible input - i.e. voter preferences. Filingpro (talk) 21:13, 7 February 2014 (UTC)

Okay, yeah, I wasn't thinking clearly. If the other models fail Unrestricted Domain, it's because they use cardinal voter models, and approval ballots don't allow for unique expression of all possible cardinal preferences. The 'other information' thing doesn't have much to do with it, except maybe in perfect info, which is a model I still don't fully understand.

Speaking of the other models, would you object if I removed the word 'strategy' from the imperfect info description? I don't know what it's supposed to communicate, since 'strategy' is basically undefined in the context of approval voting, but I suspect that it will mislead people into thinking that insincere voters are being considered in that model, when they aren't. Douglas Cantrell (talk) 22:43, 7 February 2014 (UTC)

Thanks. Yes we could remove "strategy" if we assume "rational" voters incorporate the information and potentially modify the cutoff. Filingpro (talk) 08:12, 9 February 2014 (UTC)

So do you still think Dichotomous Preferences fails Unrestricted Domain? The table hasn't been changed, but discussion on the subject seems to have stopped. Douglas Cantrell (talk) 04:04, 10 February 2014 (UTC)

Dichotomous Preferences obviously fails Unrestricted Domain because it restricts the possible input - i.e. voters' preferences, unlike the other models. Filingpro (talk) 07:47, 10 February 2014 (UTC)

It isn't productive to say that you're obviously correct about issues where we disagree. As I said before, Dichotomous Preferences doesn't prohibit any possible set of dichotomous preferences from being expressed. It also doesn't allow for full expression of ordinal preferences, but I don't think that's relevant, because preferential voting systems don't allow for full expression of cardinal preferences (see: prohibition of equal ranking) and yet they're generally said to comply with Unrestricted Domain. If I'm mistaken, I'd like to know why. Douglas Cantrell (talk) 22:49, 10 February 2014 (UTC)

A Dichotomous Preferences model means a voter with preferences A>B>C does not exist. We are changing the possible input to the voting system. In IRV, for example, a voter preferring A=B>C does exist and may vote A>B>C or vote B>A>C. We are not changing the possible input to the voting system. Filingpro (talk) 21:19, 23 February 2014 (UTC)

A voter with the preference set A=B>C only exists in IRV if you're modeling voters as having cardinal preferences. Are you saying that IRV fails Unrestricted Domain if voters are modeled as having ordinal preferences? Would 'vote only for the first name on the ballot' comply given cardinal voters? If so, in what sense is Unrestricted Domain even a voting system criterion? Douglas Cantrell (talk) 03:17, 21 March 2014 (UTC)

I see your question. If voters are modeled as having ordinal preferences this does not exclude voters that have cardinal preferences because ordinals are the more general case - i.e. cardinal voters are not excluded from the model. So IRV would not fail unrestricted domain.Filingpro (talk) 05:45, 21 May 2014 (UTC)

If your question pertains to modeling voters with strict > < ordinals excluding equal preferences, I believe this would violate unrestricted domain, because voters with certain preferences are excluded. I don't believe this is an issue of major importance but I am open to an issue that might be raised. I believe in general we often simplify the model to assume that a voter who's preference is A=B>C would toss a coin and choose either A or B (perhaps by coin toss)- if voting is considered the aggregation of how voters decide individually. Of course IRV itself does not exclude voters with equal preferences, it merely does not give them a ballot or counting method that allows them to express the equal preferences, but they can still vote.Filingpro (talk) 05:45, 21 May 2014 (UTC)

If IRV complies with unrestricted domain when voters are modeled as having unrestricted preferences, even when the expression of some preferences, e.g. A>B=C, is prohibited, then compliance with unrestricted domain isn't a property of the voting system, it's a property of the voter model. As such, I don't think it belongs in the voting system criteria table, at least so long as we continue to make a distinction between actual preferences and expressed preferences. That said, failure of unrestricted domain seems to be the reason approval voting with dichotomous preferences isn't a counterexample to Arrow's theorem, so it's probably worth mentioning elsewhere. Douglas Cantrell (talk) 23:30, 22 September 2014 (UTC)

Non-Dictatorship Relevance

The failure of non-dictatorship assuming an absolute, immovable cutoff for each voter has been acknowledged. (See section Compliance Proposal Disclosing Failure of Democratic Criteria.)

WHY NON-DICTATORSHIP FAILURE IS RELEVANT
The relevance of failing non-dictatorship has been questioned by the reasoning that the voter “chooses” the cutoff and therefore Arrow’s theorem is not relevant.

Here is why the failure of non-dictatorship is entirely not a choice by the voter (i.e. we can not say the model “allows” the voter to abstain rather than being imposed):

Simple answer: The voter does not get to choose which alternatives are in the race.

For any random alternative, the position above or below and the proximity to the absolute cutoff is completely random. Pick any two random alternatives for a two-way race. The ability for the voter to express their meaningful preference between the two is decided completely randomly. Since each voter’s criteria for determining the absolute cutoff is formulated based on their own values and vantage point, one voter can have completely arbitrary power over another voter, merely based on their different opinions. Filingpro (talk) 04:40, 27 January 2014 (UTC)

First, consensus regarding failure of Non-Dictatorship was based on your interpretation of the criterion as Arrow defined it. The validity of your interpretation, and the applicability of the original definition, isn't something I have I have a formal opinion about.

Second, that isn't the primary point I was trying to make about relevance. My primary point is that the definition of Non-Dictatorship you're using was written for a theorem about preferential voting systems, and approval voting isn't a preferential voting system. The definition may or may not be applicable, but applicability and relevance are different things.

To respond to your actual argument, voters aren't compelled to do things by the model. That isn't even conceivable; the model simply establishes which set of voters, among all possible voters, is being considered. Innate threshold includes only the infinitesimal set of voters who will always choose to approve the same candidates, regardless of who they're running against. You can think of these voters as being irrational, if you like, or maybe as having some sort of philosophical objection to expressing insufficiently strong preferences. Regardless, there's no contradiction in saying that they choose. Douglas Cantrell (talk) 09:10, 5 February 2014 (UTC)

Voters have preferences when approval voting.

Voters don't choose the candidates. The position relative to absolute cutoff is random so they don't choose whether they vote. Filingpro (talk) 21:49, 7 February 2014 (UTC)

I don't know what your first statement is supposed to mean. Are you still arguing that Arrow's Theorem is applicable, even though that isn't being contested?

Voters never choose the candidates, and the relative desirability of each candidate is always random for a given voter. We still say that they choose to express the preferences that they have, as opposed to the preferences they don't, even though they would be excluded from the voter model if they did anything else. How is this any different? If anything, you seem to be arguing that free will simply doesn't exist in an objective sense, which hardly seems relevant. Douglas Cantrell (talk) 22:33, 7 February 2014 (UTC)

Free will to choose an absolute cutoff is irrelevant when the relative position of a random alternative is randomly above or below. Does that clarify? Filingpro (talk) 08:36, 9 February 2014 (UTC)

Not really, no. Why are random preferences acceptable if a random displacement from a threshold isn't? What are we even arguing about, in terms of what should be in the article? Douglas Cantrell (talk) 03:52, 10 February 2014 (UTC)

The preferences of the voters are not random - they are meaningful to the voter, and they may be unique - i.e. each voter has their own criteria.Filingpro (talk) 05:47, 10 February 2014 (UTC)

On what grounds do you say that preferences have meaning but that a given candidate's distance from a given voter's approval threshold doesn't? Douglas Cantrell (talk) 23:17, 10 February 2014 (UTC)

The candidates are random - the voter does not choose them. A candidate falling above or below any voter's absolute threshold is random. For two random candidates, the ability for a voter's preference to be represented, or not, is random. Filingpro (talk) 21:36, 23 February 2014 (UTC)

To answer my question, you have to explain why it's valid for you to say that, yet invalid for me to say that the voters have random preferences. Douglas Cantrell (talk) 03:21, 21 March 2014 (UTC)

Are you saying the voter's absolute cutoff is chosen randomly on their behalf? I'm not sure where that leads us but I am open to explore it. I am simply saying if voters choose their absolute cutoff independently of any candidates in an election, and if they do not choose what candidates are in an election, they have no control over whether they can vote or not. For any two random alternatives, the voter's ability to vote is completely random. They have no power to decide, despite having meaningful preferences for the alternatives. Filingpro (talk) 05:16, 21 May 2014 (UTC)

I'm saying that a voter's approval cutoff is determined in precisely the same way that the voter's preferences are determined. Call that part of the model's definition, if you like. So, if the voter has cardinal preferences, and their preference for a given candidate is a random value between zero and one, then the approval cutoff will also be a random value between zero and one. If the voter has ordinal preferences, and their preference between two candidates is a 'choice', then their preference between a given candidate and the approval cutoff (i.e. A>Cutoff) will also be a 'choice.' Some voters would abstain under this model (unless it was modified to specifically exclude abstention, for whatever reason), but I consider the question of whether or not abstention is forced upon them to be meaningless.

As for where that leads us... Well, it leads us to IIA compliance and Condorcet failure. Again, I proposed this model because I thought approval voting was generally understood to have those properties. Maybe that was misguided, but given that nobody seems to have had any luck finding citations for this table, maybe the table itself is misguided. Douglas Cantrell (talk) 01:14, 23 September 2014 (UTC)

Re: Relevance: Arrow applies to voter ordinal preferences. In the table we are considering Approval when voters have ordinal preferences. Does that clarify? Filingpro (talk) 08:36, 9 February 2014 (UTC)
Re: Applicability not equal to relevance: If applicable then irrelevance requires the criterion to be irrelevant but Non-Dictatorship is obviously relevant. Filingpro (talk) 09:23, 9 February 2014 (UTC)

Relevance isn't a given, it's what I'm contesting, on the grounds that the definition you're using for Non-Dictatorship was defined within a theorem about preferential voting systems. You seem to be interpreting this as an argument about applicability every time I bring it up, but it isn't; I'm saying that Arrow's definitions aren't relevant because approval voting exists outside the scope of the theorem for which they were created. Douglas Cantrell (talk) 03:52, 10 February 2014 (UTC)

You say the argument is not about applicability but then you say "approval voting exists outside the scope of the theorem" - you seem to be contradicting yourself. Filingpro (talk) 05:47, 10 February 2014 (UTC)

Asking if Arrow's theorem applies to approval voting is a bit like asking if the power rule applies when n=0. It applies to the extent that it is explicitly inapplicable. If you want to interpret this as the theorem being inapplicable, I'd point out that an applicable definition from an inapplicable theorem is irrelevant. My main point, however, is that Arrow's theorem isn't relevant, so neither is its definition for dictatorship. Douglas Cantrell (talk) 23:17, 10 February 2014 (UTC)

Do you want to debate relevance or applicability? How about we choose one and I will respond? Filingpro (talk) 21:42, 23 February 2014 (UTC)

My main point continues to be that Arrow's Theorem is irrelevant to approval voting, and that its definitions are irrelevant as a consequence. My justification is that the theorem itself is either completely inapplicable, or applicable in such a trivial sense that it may as well be inapplicable. Douglas Cantrell (talk) 03:35, 21 March 2014 (UTC)

Since inapplicability is claimed as justification for irrelevance, I will refute innapplicability: Arrow only assumes voters have preferences and so the theorem applies to approval voting.

Given we may have reached a circularity, I am happy to let you make a final comment and I will refrain from responding if I would only be repeating myself.Filingpro (talk) 05:16, 21 May 2014 (UTC)

First of all, I skimmed through some earlier posts and noticed that I was in fact making arguments about applicability at some point, so I apologize for the inconsistency. Apparently I just decided that applicability wasn't worth contesting at some point.

Second, you technically didn't address my second point, which was that the theorem isn't relevant if it is only applicable in a trivial sense, e.g. in the sense that it deliberately exempted rated voting systems from the main theorem by categorizing them as something other than social welfare functions. Here's the relevant definition:

"Definition 3: By a "social welfare function" will be meant a process or rule which, for each set of individual orderings R₁,...,R_n for alternative social states (one ordering for each individual), states a corresponding social ordering or alternative social status, R."

Note that Arrow's individual orderings allow A>B, A>=B, and A=B. If you model voters as having dichotomous preferences, you can probably argue that approval voting is a social welfare function that fails unrestricted domain. Otherwise, for a given set of individual orderings, there are several possible social orderings, because an individual ordering like A>B>C might be counted as A>B=C or A=B>C. Social welfare functions must give a unique social ordering for every possible set of individual orderings, so approval voting isn't a social welfare function going by Arrow's definitions.

That said, Arrow's theorem is notable enough that its relationship with approval voting should probably be explained in its own section. I'm hesitant to do that without a source, however. Douglas Cantrell (talk) 01:14, 23 September 2014 (UTC)

Also, what's with the footnote on non-dictatorship under dichotomous cutoff? I can't figure out what it's supposed to mean. Wouldn't it be simpler to say 'One voter may dictate the result of the election when all other voters abstain'? I mean, granted, that sounds weird given that it's true of every voting system, but that's kind of the point I've been trying to make about including non-dictatorship on the table at all; a voter model that permits abstention is not best described as dictatorial. Douglas Cantrell (talk) 01:41, 23 September 2014 (UTC)

Thanks for the post. I do think our comments have helped illuminate the issue. I may have to study your comments further and return.

Re: requiring unique social orderings: Note that the beginning of the wiki section (which I didn't write but I believe is a correct set up) says the criteria assume the voter has ordinal preferences and therefore we look at performance when making different assumptions about how the voter chooses the approval cutoff. So in each case a voter with A>B>C leads to a unique outcome depending on the cutoff model. (The model we assume of the voters determines any single instance we are considering - i.e. set of approval ballots). I believe in each case our models are deterministic - i.e. the same set of voters having the same preferences and information about other voters etc. always returns the same unique result.

Re: all voting systems that allow abstention are 'dictatorial': In IRV, with a voter preferring A>B and another voter preferring B>A, what is your conceptual model under which one of the voters abstains? How do you arrive at Arrovian dictatorship? I don't see that but I am open to argumentation.

Filingpro (talk) 11:58, 3 November 2014 (UTC)

Example Approval Majority Failure Elects Extremist Not Consensus Candidate

Voters vote for any number of available locations (e.g. x, y, z). Voters vote cooperatively without knowing how others might vote, and so they approve only locations closer than average distance among the available options. We might instead suppose there is an objective judge that measures the distance of each voter to the available locations, and to ensure fairness approves for each voter any location closer than the average distance. In this way we ensure there is no possibility of strategic voting.

There are 54 voters at location A.
There are 45 voters at location B.
There is 1 voter at location C.

+++++++++++++++

+++++++++++++++

+++++++++++++++

+++++++++++z+C+

+++++++++++++++

++++++++A++++++

++++++y++++++++

+++++++++++++++

+++++++++++++++

+++++++++++++++

+++++++x+++++++

+++++++++++++++

++++++++B++++++

+++++++++++++++

+++++++++++++++

Race between x, y, and z:
54 A Voters (y:2.24, z:3.61, x:5.1), average distance = 3.65, approve yz
45 B Voters (x:2.24, y:6.32, z:9.49), average distance = 6.02, approve x
1 C Voter (z:2, y:7.62, x:9.22), average distance 6.28, approve z

Extremist 'z' is the winner, despite 'y' is the centrist candidate and the majority winner, and 'y' defeats 'z' pairwise 99:1!

We need to update this paragraph from the article:
Approval voting fails the majority criterion, because it is possible that the candidate most preferred by the majority of voters, for example, winning 60% in a plurality election, will lose, if 65% indicate another candidate is at least acceptable to them. If 40% strongly dislike candidate A but like candidate B, and 60% mildly prefer candidate A over candidate B, approval voting might elect candidate B, whereas plurality would elect candidate A in a two candidate race.
The paragraph implies that Approval voting's failure of the Majority Criterion is only due to the voting system's ability to measure strength of preference, rather than just ordinal preference. But as the counterexample above shows, Approval voting's failure of the Majority Criterion can mean just the opposite, a complete lack of ability to detect the strength of preference of the electorate, even when voters vote non-strategically - i.e. in a cooperative fashion. Filingpro (talk) 09:35, 27 January 2014 (UTC)

It's a bit silly to call optimal strategy with zero-information 'non-strategic' or 'cooperative,' but I suppose that's insubstantial.

In the example you gave, the preference that A voters had for y over z was substantially weaker than the preference that the C voter had for z over y, which is exactly what the quoted paragraph describes, and an example of the results being influenced by the strength of preferences. Specifically, that A voters were less influential than C in the contest between y and z despite being more numerous is a consequence of their decision to prioritize opposition to x, which was itself a consequence of a relatively weak preference for y over z. Douglas Cantrell (talk) 09:54, 5 February 2014 (UTC)

The electorate prefers y to z with strength 216.63, and z to y with strength 5.62. Filingpro (talk) 21:42, 7 February 2014 (UTC)

That doesn't contradict anything I said. Here's the paragraph you quoted, with the numbers and variables modified so that it's applicable to your example:

"Approval voting fails the majority criterion, because it is possible that the candidate most preferred by the majority of voters, for example, winning 54% in a plurality election, will lose, if 55% indicate another candidate is at least acceptable to them. If 1% strongly dislike candidate y but like candidate z, and 54% mildly prefer candidate y over candidate z, approval voting might elect candidate z, whereas plurality would elect candidate y in a two candidate race." Douglas Cantrell (talk) 22:38, 7 February 2014 (UTC)

Correction: 99% prefer candidate y over candidate z, Approval elects z.

I object to the sentence A:[Approval fails Majority] because B:[Approval measures strength of preference] - i.e. A because B is incorrect WP:SYNTH.

Example Approval fails majority despite strength of preference of electorate and individual voters:

V1: A100, B51, C25, D0, approves AB

V2: A100, B51, C25, D0, approves AB

V3: C100, B51, A49, D0, approves B

A is majority, Approval elects B.

B preferred with strength 2 by one voter, despite A preferred with strength 49 by two voters.

Infinite range voting 0-1, when voters calibrate the highest preference 1 and lowest 0, satisfies Majority and measures strength. Measuring strength doesn't cause failure of Majority criterion.

Suggestion: Change the paragraph to explain that Approval can elect a candidate that is a more of a consensus candidate - i.e. acceptable to larger than a majority, unlike Plurality voting. Also point out that Approval can fail to detect preferences, and elect a minority candidate when Plurality would elect the majority, to avoid bias in the article.Filingpro (talk) 06:23, 9 February 2014 (UTC)

Strictly speaking, only 54% had a mild preference; the preference of B voters was of moderate strength. That said, I suspect you could create an example where their preference was mild as well, so it would be more precise in a general sense to say that "at least 54% only mildly prefer candidate y over candidate z".

Approval voting wasn't said to fail Majority because it measured strength of preferences, it was said to fail because it doesn't necessarily elect the candidate which Majority requires it to elect given a specific set of conditions. It does seem to be implied that the specified conditions must be met for Majority failure to occur, and you've now shown that they do not.

Score voting is never Majority compliant given rational zero info voters. Never mind, you noticed. I need to stop reading your posts from the edit page.

Consensus candidates and minority candidates aren't mutually exclusive, and equality in the number of favorable and unfavorable comparisons doesn't seem like balance of a sort which is particularly desirable. Anyway, I would propose the following paragraph. If you have a counter-proposal, please post the actual text so that I can give it proper consideration.

"Approval voting fails the majority criterion, because it is possible that the candidate most preferred by a majority of voters will lose. For example, if a candidate would receive 60% support in a plurality election, the same candidate might be defeated under approval voting if 65% of voters indicate that some other candidate is at least acceptable to them. This might happen because 40% strongly prefer candidate A to candidate B, while 25% only have a weak preference for B over A, relative to some third candidate C." Douglas Cantrell (talk) 10:10, 9 February 2014 (UTC)

Thanks for working on this - quick comments and I may return within a day or so...looks much better. In "For example" I wonder if it would be helpful to the reader to introduce "B" in that sentence - to connect it to the later sentence. I am open to saying "strongly" and "weak" when we clarify "might happen", but it may also be important to point out that the outcome may have nothing to do with the relative strength but the rather arbitrary position relative to the cutoff, as shown in the example I have above where B preferred with strength of 2 and A preferred with strength of 49 (also by more voters). Filingpro (talk) 17:31, 9 February 2014 (UTC)

There is still a general problem with the rhetorical structure: [1. Approval fails Majority criterion. 2. For example, the stronger preferences prevail.] It leads the reader to think this is why Approval fails Majority. But the problem is that Approval can fail majority when failing to measure strength of preferences. Suggestion: Rewrite the paragraph to merely say that Approval voting can measure strength of preference under certain circumstances when Plurality cannot, and then provide a clear example readers can understand. Filingpro (talk) 07:09, 10 February 2014 (UTC)

The second sentence is actually a very general explanation of why approval fails: A candidate with strong support from a majority can be defeated by a candidate with adequate support from a larger majority. I'm pretty sure that covers every scenario where failure is possible, and it's something that might not be immediately obvious to those with a naive understanding of majority rule.

The third sentence goes into more detail, and is less generally applicable as a result. I thought I was able to make that reasonably clear, although it might be better to change sentence two so that it's a fully general explanation, just for the sake of contrast with sentence three. I'm hesitant to place especially great emphasis on the scenarios where sentence three isn't applicable, if we aren't going to explain why failure occurs in those cases. I'm pretty sure approval's centrist bias is the cause, but that might be difficult to explain. Douglas Cantrell (talk) 00:16, 11 February 2014 (UTC)

Agreed re: second sentence. I like that. The first is basically a definition of the criteria - thats ok too. Can you explain how the A, B, C in the third sentence relates to the second? I think I am not clear. Overall it seems to be improving from the prior posting. Thanks. Filingpro (talk) 22:18, 23 February 2014 (UTC)

Candidate A is 'some other candidate' in the second sentence, while B is the one that would win in a plurality election. Douglas Cantrell (talk) 04:43, 21 March 2014 (UTC)

It may also be worth mentioning that a majority faction can guarantee its favorite candidate wins under approval voting, as long as the majority group recognizes that it exists. For example, if pre-election polls ask, “Who is your favorite candidate?” and one candidate achieves a true majority, then their supporters can simply bullet-vote for only that candidate in the election. Qaanol (talk) 03:43, 7 March 2014 (UTC)

"Approval voting fails the majority criterion, because it is possible that the candidate most preferred by a majority of voters will lose. For example, if a candidate would receive 60% support in a plurality election, the same candidate might be defeated under approval voting if 65% of voters indicate that some other candidate is at least acceptable to them. This might happen because 40% strongly prefer the second candidate to the first, while 25% only have a weak preference for the first over the second, relative to some third candidate. If the latter group does not prioritize opposition to the third candidate, choosing instead to express their preference for the first, then majority failure will not occur." ? Douglas Cantrell (talk) 04:41, 21 March 2014 (UTC)

I think you made improvements. I think I may still be lost because I don't know which candidate is first and second by the time I get to the third sentence. Perhaps this kind of discussion really needs to be shown as an actual profile of voter preferences and approvals. I may have to abstain from this for a while because I still see the main problem is what is central thesis of the paragraph? The problem is that I believe the original purpose was to offer an excuse for failure of the majority criterion and portray this as a feature of the voting system. At the moment, it seems the paragraph reads the strongest when it stops after second sentence. To be clear, I am not opposed to portraying positive aspects of approval voting. Can we take an editorial step back, what is the actual point we are trying to make here? For example, if we want to say something positive about approval measuring strength of preference etc. I support that. But, if we are talking about failure of majority, we can't pick the most innocent case that makes the voting system look good and exclude the damning cases (as the example I gave above). Filingpro (talk) 06:04, 21 May 2014 (UTC)

It's not about which examples make the system look good or bad. The priorities for the example should be that: it makes the necessary point; as simply as possible; and that it's as plausible as possible in a real-world election, consistent with the first two points. I think the example we're using here is reasonably good on all three points. I do agree, though, that it's currently too hard to keep track of "first" and "second" candidates... should we give them letters? Homunq (࿓) 13:10, 21 May 2014 (UTC)

I believe I updated the paragraph to convey what everyone is trying to say. Filingpro (talk) 20:08, 27 September 2015 (UTC)

In the example, the "average" was arbitrarily chosen as the cutoff. However, there is no basis for that choice, hence the whole example falls. A voter might just as well choose "only the nearest" or "everyone but the furthest" and get different outcomes. Saying that "of people vote on a certain way, they get what that certain way says they get" seems to me to not be a weakness. Jwatte (talk) 05:54, 20 April 2020 (UTC)

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Doodle.com ?

Doesn't www.doodle.com arguably use a version of the approval voting system? If so, should we mention it? 130.88.16.117 (talk) 12:02, 10 April 2014 (UTC)

Edits To Strategy Overview

Homunq I am open to your edits. For the reasons below I edited and perhaps we can improve...

The paragraph you added at top:

"If a voter knows exactly how all others will vote, and if their preferences for different tie results are optimistic, pessimistic, or utility-maximising, then there are no insincere approval strategies; that is, in order to get a better result, there is never a need to approve a less-favored candidate while disapproving a more-favored one. However, if voters have limited knowledge of others' preferences, there are certain rare cases when a minority of voters can get a tiny advantage through an insincere vote."

(1) I see a problem with the basic rhetorical structure:

If [voters have perfect info] then [all votes are sincere]. If [voters have imperfect info.] then [there are insincere votes].

(2) Why are we starting the strategy Overview section with "when voters have perfect information...?" When voters have perfect information, doesn't every voter who supports the Condorcet winner bullet vote, for any voting system that allows truncation? I don't understand your point or what this tells us.

(3) "preferences for different tie results" Aren't tie results rare? If the voter has perfect info, do we really need to put in the first sentence, in the Overview, the near impossible boundary case where a voter's 1st choice and last choice are tied, and they are debating whether to approve the second choice which also happens to tie? Really? Why put that here?

(4) "IF preferences for different tie results are optimistic, pessimistic, or utility-maximising" - what else can they be if not optimistic, pessimistic etc.? Must the first sentence of the Overview be so complicated? Are you saying unless the preferences for ties have one of these three qualities, the votes are no longer "sincere"?

(5) "get a tiny advantage" - what do you mean? Changing the winner of the election?

(6) "certain rare cases" "tiny advantage". Lets be more scientific about this, if you like. I suggest we find, for example, a statement from Brams for why Approval is less manipulable than other systems and a summary of his reasoning for it. We should also site Jack H Nagel on the issue with the Burr Dilemma where strategy can lead to instability and poor outcomes.

The qualification that Bullet-Voting and Compromising can be done "sincerely" and Push-Over and Burial are necessarily insincere, has several problems:

(7) The fact that Bullet-Voting and Compromising can be done "sincerely" has to do with Approval voting properties and because Approval voting happens to be vulnerable to these strategies (e.g. Compromise in ranked methods uses ordinal reversals). Its not related to how problematic or damming the strategies are themselves, as you ingeniously imply. I would argue that Bullet Voting and Burying are the worst from a strategic voting standpoint, because they can lead to instability. Lets not have that argument here.

(8) It sounds like an oxymoron, these strategies can be done "sincerely". I think that's confusing and just doesn't make sense. The point about every Approval vote being "sincere", by a certain definition, should stand on its own. It shouldn't then be misconstrued to imply a judgement about which strategies are "sincere" and which are insincere.

(9) I object to making qualifications on the strategic voting until we first state what the strategies are. (Then we might talk about whether these strategies are "sincere" etc.)

Therefore I moved, and rewrote, what I could ascertain from your post, at the bottom of the Overview section.
Filingpro (talk) 06:41, 5 September 2014 (UTC)

Section Other Issues & Comparisons - Problem "Centrists" "If Voters Are Sincere"

Re: the current entry:

"If voters are sincere, approval voting would elect centrists at least as often as moderates of each extreme. If backers of relatively extreme candidates are insincere and "bullet vote" for that first choice, they can help that candidate defeat a compromise candidate who would have won if every voter had cast sincere preferences."

Many problems. Briefly, we define every approval vote in the article to be "sincere". What is a sincere vote? I don't know.
We need to fix this I don't have time right now. Quick suggestion:

When enough voters set their approval cutoff to approve more than one candidate, approval voting can elect a centrist candidate in common cases where plurality voting elects a minority candidate (due to vote splits). Approval voting can also elect a centrist candidate in certain cases where Instant-Runoff Voting may eliminate such a candidate in early rounds of counting.

The devil is in the details here. As has been shown in other post on this talk "Approval Elects Extremist Candidate." Sometimes plurality can elect a centrist candidate when approval does not. How do we make this statement more scientific? Do we need to refer to single peaked preference simulations as per doctor Ka Ping Yee? To be clear, I support making a statement regarding approval voting's potential to elect centrists. It needs to be stated accurately. I think the above direction is an acceptable remedy.

Also the following entry needs examination/qualification:

"If voters are sincere, candidates trying to win an approval voting election might need as much as 100% approval to beat a strong competitor, and would have to find solutions that are fair to everyone to do so. However, a candidate may win a plurality race by promising many perks to a simple majority or even a plurality of voters at the expense of the smaller voting groups."

I propose:

A candidate competing in an approval voting election might need as much as 100% approval to defeat a strong competitor, and would have to find solutions that are fair to everyone to do so. In contrast, a candidate may win a plurality race by promising perks to a simple majority or even a plurality of voters, at the expense of the smaller voting groups.
Filingpro (talk) 21:15, 27 September 2015 (UTC)

Section Other Issues & Comparisons - Problem "reversed as disapproval voting"???

I don't know what this statement means:

"Approval voting without write-ins is easily reversed as disapproval voting where a choice is disavowed, as is already required in other measures in politics (e.g., representative recall)."

I propose removing it as it seems to be redundant to the statement regarding approval allowing voters to vote against. Approval voting may have similarities to "representative recall" but it is not. I don't see its relevance here?

Filingpro (talk) 21:24, 27 September 2015 (UTC)

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References

ambiguous crosses

On an approval ballot, the voter can select any number of candidates.

This image on the article unknowingly highlights a problem with using crosses on yes/no approval ballots.

This is an old issue, referred to for example in https://www.researchgate.net/profile/Graeme_Orr/publication/29454591_The_Conduct_of_Referenda_and_plebiscites_in_Australia_A_legal_perspective/links/53db0c2c0cf2a19eee8b43ff/The-Conduct-of-Referenda-and-plebiscites-in-Australia-A-legal-perspective.pdf

Mixed ticks and crosses unambiguously mean yes for the ticks, no for the crosses, but in isolation a cross is ambiguous.

Is there a better example of an non-ambiguous completed approval ballot? --SmokeyJoe (talk) 03:15, 29 March 2018 (UTC)

Clearer description of 2016 Independent Party of Oregon election?

Until yesterday, this was characterized as:

Approval voting has been used in binding multi-jurisdiction elections for public office by the Independent Party of Oregon in 2011, 2012, 2014, and 2016. Because Oregon is a Fusion voting state, many legislators and statewide officeholders have been cross-nominated using the method.(citation)

As of a recent edit by 108.28.185.80, it now says:

Approval voting has been used in privately administered nomination contests by the Independent Party of Oregon in 2011, 2012, 2014, and 2016. Oregon is a Fusion voting state, and the party has cross-nominated legislators and statewide officeholders using this method; its 2016 presidential preference primary did not identify a potential nominee due to no candidate earning more than 32% support.(3 citations)

The first description fully respects the Independent Party of Oregon process, which appears to have won a court battle to protect their privately-administered election. It does, however, paper over the fact that this isn't a traditional publicly-administered election. The second description clarifies that it's "privately administered", but then also refers to it as a "contest" rather than "election". It adds two new citations, and inserts additional information about the "2016 presidential preference primary", citing a FairVote editorial criticizing Approval Voting.

Is the bit about the 2016 presidential preference ballot useful information to include? Are the three citations now present the best sources to include? Anyone have the time+energy+knowledge for a more concise, helpful, and neutral description of that election? -- RobLa (talk) 04:23, 26 June 2018 (UTC)

UN Vote

Is it true that Shashi Tharoor "had the highest overall approval rate" in the UN straw poles? His own wikipage says no. — Preceding unsigned comment added by LebanoGranado (talk • contribs) 08:58, 6 March 2019 (UTC)

Thanks for the query, LebanoGranado. I added the following ref. here and at 2006 United Nations Secretary-General selection, but not at Shashi Tharoor:

• Tharoor, Shashi (October 21, 2016). "The inside Story of How I Lost the Race for the UN Secretary-General's Job in 2006". OPEN Magazine. Retrieved 2019-03-06. {{cite web}}: Cite has empty unknown parameter: |dead-url= (help).

Sincerely, HopsonRoad (talk) 13:43, 6 March 2019 (UTC)

Approval with runoff elections

I am trying to find more information about the use of two-term runoff voting with approval voting being used for the first term. I assumed that there was more research done about this subject, but all I could find was a proposal to implement it in the city of St. Louis. I also found a forum post that briefly mentions it along side a visualization, but that's it. — Preceding unsigned comment added by Monotype97 (talk • contribs) 15:58, 26 May 2020 (UTC)

As it turns out, there is already a page for this: Unified Primary. Monotype97 (talk) 16:11, 26 May 2020 (UTC)