Talk:Approval voting

Removal of Entire Subsection "Compliance with .. Criteria"

I know this may seem like a big edit but I think that this section adds absolutely nothing of value to the article. it is full of ambiguous usage of technical terminology that could mean many different things under different interpretations, and even with the most generous of interpretations most likely constitutes OR. The list of "criteria" are certainly real things that might be considered about a social choice rule, but this is an article about Approval voting not an article about "list of criteria for election rules." also many of the pass-fail entries in the table are not even correct.

absent strong protest I will remove this section. if someone wants to re-add it please do so in way that uses technically unambiguous terminology and provides proper citations, and is relevant to specifically Approval voting as a rule. Affinepplan (talk) 14:43, 21 October 2024 (UTC)

Note that this was done and partially reverted and citations were provided. McYeee (talk) 23:27, 21 October 2024 (UTC)

yes, I saw the citations (and have read them). I don't think they suffice. As just a example nitpick (and certainly not the entirety of problems with the section) the reference to "Strategyproof" does not specify whether it refers to the absence of profitable manipulations for individual agents, for coalitions of agents, or for strategic candidate entry / exit, nor does it specify whether such manipulations are deterministic or if they are in expectation, etc.

also the phrasing "There is no ultimate authority on which criteria should be considered, but the following are criteria that many voting theorists accept and consider desirable:" is indicative of a non-academic author. an academic perspective will be more objective and neutral about "criteria" and more generally behavior of an election rule, rather than thinking only of which voting rules are "acceptable" Affinepplan (talk) 23:36, 21 October 2024 (UTC)

Do you have a wording you prefer to "There is no ultimate authority on which criteria should be considered, but the following are criteria that many voting theorists accept and consider desirable"? For strategyproofness, does that distinction actually matter? McYeee (talk) 23:41, 21 October 2024 (UTC)

yes my preferred wording would be to delete that clause entirely.

if someone wants to add a technically sound and more thorough section "Approval Voting #Manipulability" that could be fine. but as-is this does not suffice Affinepplan (talk) 23:44, 21 October 2024 (UTC)

Are you aware of any reliable sources contradicting the table? McYeee (talk) 00:05, 22 October 2024 (UTC)

are you aware of any supporting it? like I said, the citations provided do not suffice. the burden of proof is on the author of the content. Affinepplan (talk) 00:40, 22 October 2024 (UTC)

I understand the burden. I only asked because you said "many of the pass-fail entries in the table are not even correct". McYeee (talk) 02:06, 22 October 2024 (UTC)

I should rephrase that to some combination of "needs context," "needs citation," "so vague as to be unfalsifiable," and in the case of IIA, is plain wrong. This article states multiple times that Approval can fail IIA. This is simply mathematically incorrect and is a common misunderstanding of IIA among the "reformer" crowd (this is a particular internet community interested in election rules that usually quarantines their pseudoscience to mailing lists and https://electowiki.org/wiki/Main_Page ) Affinepplan (talk) 02:15, 22 October 2024 (UTC)

I read that cell as saying that as saying that with approval voting, violations of IIA cannot occur when all preferences are dichotomous. Is that not how you read it? McYeee (talk) 02:38, 22 October 2024 (UTC)

with approval voting, violations of IIA cannot occur full stop. Affinepplan (talk) 02:44, 22 October 2024 (UTC)

Do you have a source for that? McYeee (talk) 02:45, 22 October 2024 (UTC)

this is a well-known fact, but I suppose if you need a source you could use this https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2239118 (just one of the first I found on the topic on G Scholar) Affinepplan (talk) 02:48, 22 October 2024 (UTC)

another source would be this paper https://www.ijcai.org/proceedings/2018/47 showing that all Thiele rules satisfy IIA (of which Approval is a member) Affinepplan (talk) 02:51, 22 October 2024 (UTC)

The first source explicitly says it's working with dichotomous preferences. The second says it's "defin[ing] three axiomatic properties", which makes me think that we can't use that paper, to argue that the dichotomous preference definition of IIA is standard. I guess the standardness of the Dichotomous preference definition of IIA is kind of the point of dissagrement between you and Lime. I think that unless more sources are produces, WP:V says you're right. McYeee (talk) 03:33, 22 October 2024 (UTC)

that is a very well-established definition. the wording "we introduce" is just a writing style artifact and should not be interpreted as a claim of originality from the authors. Affinepplan (talk) 07:05, 22 October 2024 (UTC)

I get that it's a not a claim of originality, but it's also not a claim of non-originality. In any case, I haven't seen sources for any other definition, so it's kind of a moot point. McYeee (talk) 21:10, 23 October 2024 (UTC)

Concur w/ @McYeee neither source establishes Approval satisfies IIA, without violating Unrestricted Domain, i.e. imposing dichotomous preferences. Filingpro (talk) 07:30, 10 February 2025 (UTC)

of course, my rather strong tentpole planted there ^ depends on how precisely IIA is being defined in this context. I am using the typical defintion. if the author wishes to use an atypical definition in order to make themselves correct (I do not generally recommend this behavior) then they must do so explicitly. Affinepplan (talk) 02:45, 22 October 2024 (UTC)

I don't see that Approval can satisfy IIA. Axiomatically an election chooses certain alternatives at the exclusion of others. It's not an Amazon rating system. If we allow voters to vote for their preferred alternative in a two-way contest, and there is no dictator, I don't see how we can maintain independence as we start adding and removing candidates. Filingpro (talk) 07:42, 10 February 2025 (UTC)

you are either misunderstanding what IIA is or working with an incomplete / underspecified definition in your mental model. I think this whole subsection is just an issue of [[WP:Competence] Affinepplan (talk) 18:27, 10 February 2025 (UTC)

I understand IIA to mean adding and removing candidates should not change the outcome between any pair of alternatives. For Approval to pass IIA we have to enforce that some voters cannot vote for their preferred candidate, because any voter who approves candidate A, and not B or C, must abstain in a two-way contest between B and C. Do you see the problem? Filingpro (talk) 04:30, 11 February 2025 (UTC)

your understanding is incomplete. please read

https://www.ijcai.org/proceedings/2018/47 or https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2239118 as I linked above

your note about unrestricted domain is simply not relevant as this is not a condition of IIA. and in the Approval setting one typically assumes dichotomous preferences anyway (otherwise you must assume some model of behavior given non-dichotomous preferences)

if you are not an expert in the topic please refrain from blocking edits that will make wikipedia better. Affinepplan (talk) 16:07, 11 February 2025 (UTC)

Can you provide a more specific citation for the claim that "in the Approval setting one typically assumes dichotomous preferences anyway"? It's not at all obvious to me that "assum[ing] some model of behavior" isn't just as common in the literature. McYeee (talk) 19:42, 11 February 2025 (UTC)

please understand this is simply how IIA is formalized. "assuming some model of behavior" may be very common for some questions but not to answer the question "what is IIA" or "does this rule satisfy IIA"

this entire discussion is a WP:Competence issue. I really don't think any of you guys understand what IIA is. Affinepplan (talk) 22:03, 11 February 2025 (UTC)

IIA has been formalized in at least two different ways in the literature. I don't see why we should ignore that. McYeee (talk) 22:55, 11 February 2025 (UTC)

The experts are Gibbard and Satterthwaite. If we assume dichotomous preferences then Approval is a perfect, strategy-proof method, contradicting the experts.

@Affinepplan I heed your concern about WP:competence and take that seriously. I will review further the articles you cited and compose a reply. At the outset from what I can tell the contributors in this discussion are open minded to your opinions and interested in what you have to say, so there may not be major concern of someone being incompetent and also not being aware.

To clarify, is it your position that anyone who challenges the claim that approval voting satisfies IIA under any legitimate voter model is incompetent and unaware of their incompetence?

Thank you, Filingpro (talk) 23:57, 11 February 2025 (UTC)

I apologize for coming off strong with the hostility -- I can see you are taking this seriously.

unfortunately many of these social choice related pages are plagued with editors who have only a extremely minimal understanding of the field and often appeal to pseudoscience, self-published works, or in the worst case politically-motivated sophistry

so the argument on this article specifically about IIA, to me is lumped in with an unending and very frustrating argument across dozens of articles attempting to get people to take academic rigor seriously

it is not my position that "anyone who challenges the claim that approval voting satisfies IIA under any legitimate voter model is incompetent"

however, it IS my position that a certain level of mathematical maturity (maybe mid-undergraduate?) is necessary to properly formalize things like IIA. and that every formalization I have seen thus far in the literature leads one to conclude that either Approval satisfies IIA, or that IIA is not an applicable concept to Approval. But one does not conclude that Approval outright fails IIA

and it is also my position that an *unwillingness* to engage with existing literature and rather work off of speculation or fantasization is indistinguishable from incompetency. Social choice is *math* and questions about technical statements should not be treated like a popularity poll in the talk page. So it is really irrelevant how many other editors chime in one way or the other when the vast majority of them have no expertise to comment.

However, I admit that I have assigned you into an amalgamation of such commenters, which you do not deserve. so if you'll allow me I'd love to take the chance to reset the tone of this discussion:

at this time, do you have reason to believe that Approval fails IIA? if so, could you please be very specific and technical about how exactly you are defining those terms? (both "Approval" and "IIA"). And ideally, could you provide references to published works of research making use of these definitions? Affinepplan (talk) 03:48, 12 February 2025 (UTC)

In the formulations where IIA is not an applicable concept to approval voting, it is an applicable concept to the function composition of the Leader rule and approval voting. Didn't we already have this conversation? McYeee (talk) 20:19, 12 February 2025 (UTC)

for example, https://shs.hal.science/file/index/docid/121751/filename/stratapproval4.pdf is provided as a reference for the claims about the "trembling hand" equilibrium, but this paper does not even contain the words Independence of Irrelevant Alternatives (IIA), let alone discussion of Approval's compliance.

The row for "Zero Information" links to Impartial culture , but that is quite an orthogonal concept altogether. Zero information refers to a model of agents' beliefs, but impartial culture refers to a model of agents' preferences. Furthermore, the citation provided for this row (the Myerson Weber paper) absolutely does not support the claims made in the table and has nothing to do with "Zero Information," in fact the proofs in the Myerson Weber paper specifically rely on proving the existence of a very particular set of agents' beliefs. And of course it goes without saying that this paper doesn't touch at all on the "criteria" the author here is suggesting it does Affinepplan (talk) 00:56, 22 October 2024 (UTC)

I repeat, if someone wants to re-add it please do so in way that uses technically unambiguous terminology and provides proper citations

@McYeee I hope you can see that this has not been achieved, and will agree with my decision to re-remove this section after another day or two has passed to gather feedback. Unfortunately I have had very bad experiences in the past with this particular author in content disputes and I do not think they will be receptive to criticism or correction, so we'll have to gather consensus here without them. Affinepplan (talk) 00:58, 22 October 2024 (UTC)

I agree that the current citations are insufficient. If no more sources are added, removing the section makes sense without prejudice to reinsertion with better sources. If sufficient sources are added, I think the ambiguity issue is fixable without deleting the section. McYeee (talk) 02:18, 22 October 2024 (UTC)

I don't have any prejudice for the idea behind the section, of course. but it would need substantial explication, not just a different set of footnotes. Affinepplan (talk) 02:55, 22 October 2024 (UTC)

To be clear, I was not accusing you of prejudice. I meant without prejudice (legal term). McYeee (talk) 03:36, 22 October 2024 (UTC)

Archiving

I think we should move old discussion to an archive. Does anyone have any preferences on the details of that, or any objection to it? McYeee (talk) 23:29, 21 October 2024 (UTC)

Improve Binary Preference Note?

Current text of footnote: " Assuming voters have only two categories of preference ("approve" and "disapprove"). This can be a good approximation of preferences in a two-party system, or when voters are highly-polarized. "

Q: Is there at least one empirical election example to support the claim "this can be a good approximation"?

Q: Can we be more scientific in our assertion, i.e., how good is "good"? Can we quantify that? If this is an opinion, then should we disclose the opinion-holder? Would it be better to say "This might approximate..."

Q: If voters are binary, aren't the candidates too? If so, then who is the third candidate, a clone? Why would they run in the election?

Q: Is it logically possible to have an an electoral system based on approval voting that is a two-party system? Do we mean to say "when there are two dominant political parties"?

One approach might be to omit the claim in the second sentence. But this begs the question as to the relevance of the row "binary preference" in the compliance table.

A central problem may be that imposing binary preferences on voters violates an axiom in social choice theory—that voters may have meaningful preferences among the alternatives. Specifically if a voter may prefer any two candidates A > B, then for any unique candidate C, the voter may have a preference between C and A and/or C and B. ~ Filingpro (talk) 05:59, 10 February 2025 (UTC)

I agree, it seems a bit of a muddle. I think the binary preferences category is intended to show what happens if the voters have an absolute scale, and every candidate they can think of is either unambiguously approved or unambiguously disapproved. In this setting, approval passes IIA because the scale stays the same no matter who is running.

But the footnote seems to refer to a more general situation where every voter either likes or dislikes a candidate, which does roughly map to a two-party or dominant-party situation. But here we don't know if the scale is absolute. Suppose that an act of nature makes one of the major party candidates drop out, then it's possible that even in such a situation, voters who like one of the third parties would switch from approving the other major candidate to approving only the third party candidate. Such voters reveal themselves to not actually have binary preferences.

IMHO, the easiest way to solve this is probably to just change the footnote to no longer refer to two-party situations. But then your point holds that it's far from clear how the binary preferences row is important. It may be of theoretical interest, as it does show when Approval passes IIA. But practical elections would only approximate such a setting, and "only approximately passing IIA" is still a failure of IIA proper. So maybe deleting the row is the better option. I'm unsure. Wotwotwoot (talk) 16:54, 10 February 2025 (UTC)

Yes I agree a voter’s binary preference for a candidate could not change by adding or removing other candidates. The voter would have to change their single, binary criterion, implicating either a second criterion or a criterion having a matter of degree, either of which makes strict binary preferences impossible.

So yes I believe binary preferences are absolute in the above sense, although not scalar.

I am open minded but not persuaded that a binary preference model maps to polarized or two-party dominated environments. The U.S.A. is considered a polarized two-party climate, yet I recall numerous polls where supermajorities of voters expressed disapproval of both parties and the need for a third party.

I also agree imposing an absolute cutoff when voters have cardinal preferences would also achieve IIA. Unlike binary preferences, this model satisfies Unrestricted Domain although fails Non-Dictatorship, whether defined for ordinal or cardinal preferences, in my assessment. The reason is because we would have to force some voters to abstain in two-way contests, even if their strength of preference is greater than another voter who has a negligible, opposing preference but straddles their cutoff. For that reason as a scientific model I don’t think absolute cutoff is predictive, even for trivial elections. At least, it’s a limited predictive model, I would say.

Editorial suggestion below. Filingpro (talk) 23:29, 11 February 2025 (UTC)

The page on unrestricted domain says that it implies that preferences (and only preferences) are used, so cardinal methods fail UD by definition as far as I understand. That's what makes Arrow's theorem inapplicable to rated methods.

As for dictatorship, a method is dictatorial if there is a privileged voter who, no matter what others do, can force the outcome to whatever they'd prefer. The cardinal methods aren't dictatorial by that measure since, even though the voters' expression may be restricted, it's not restricted in such a way that someone else can force (dictate) the outcome regardless of what the other voters vote. Wotwotwoot (talk) 19:29, 12 February 2025 (UTC)

Thanks @Wotwotwoot

Suggested remedy: Authenticate the published author who holds the opinion, for example, “Voting theorist Steven Brams suggests binary preferences approximate voters opinions when… [insert appropriate wording representing Bram’s actual claims and add footnote with link to his paper]” Filingpro (talk) 23:26, 11 February 2025 (UTC)

I've removed the claim that binary absolute preferences are a good model for polarized or two-party/majority-party electorates, since I'm not aware of any papers stating this. That doesn't mean there isn't any, but I'll leave the source hunting to anybody who'd like to add it back in. Wotwotwoot (talk) 19:25, 12 February 2025 (UTC)