[EM] Semantics of voting

Sun Mar 6 20:50:36 PST 2022

Hey Colin, I don't have much to add to this discussion, but I wanted to ask if you're familiar with some of the work cited in the Accuracy section of the Wikipedia article on the Spatial Model of Voting:

https://en.wikipedia.org/wiki/Spatial_model_of_voting#Accuracy

I think there's some good support there for the spatial model.

PS I love your post about comparing different voting systems. I'm working on a toy to compare (and visualize) voting system outcomes as well, but it's only up to 2 dozen systems so far. Check it out:

https://votevote.page/

Voters and candidates are all colors and voter preference is calculated as the distance between a voter and a candidate (it's an average of RGB and HSL distance for now, but I'd like to make this more customizable soon).
Mar 6, 2022, 1:02 PM by election-methods-request at lists.electorama.com:

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> Today's Topics:
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>  1. Re: Semantics of voting (Kevin Venzke)
>  2. Re: Semantics of voting (Colin Champion)
>  3. Tactical voting under a jury model (Colin Champion)
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> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sun, 6 Mar 2022 05:56:13 +0000 (UTC)
> From: Kevin Venzke <stepjak at yahoo.fr>
> To: EM <election-methods at lists.electorama.com>,  Colin Champion
>  <colin.champion at routemaster.app>
> Subject: Re: [EM] Semantics of voting
> Message-ID: <1465719469.329608.1646546173987 at mail.yahoo.com>
> Content-Type: text/plain; charset=UTF-8
>
> Hi Colin,
>
> Le mardi 1 mars 2022, 11:04:13 UTC?6, Colin Champion <colin.champion at routemaster.app> a ?crit : 
>
>> I started drafting a post on this subject, but it got longer and longer 
>> so I turned it into a web page: 
>> http://www.masterlyinactivity.com/condorcet/semantics.html
>>
> >? ? Briefly, I argue that discussions of voting methods are only 
> >?meaningful if a semantics can be attached to the correctness of 
> >?electoral decisions; that models (such as jury and spatial models) can 
> >?provide such a semantics, leading to a Bayesian interpretation of 
> >?correctness; that the logical criteria stand or fall according to 
> >?whether they can be validated under a suitable semantics; that some 
> >?stand, some fall, and some are best seen as statistical approximations.
>
> >??? The topics I discuss are ones I have not seen addressed elsewhere. I 
> >?have no idea how new my ideas are, or whether, if I was better grounded 
> >?in the field, I'd have been able to discuss the subject with greater wisdom.
>
> I read through this a few times. I think I understand most of it, other than the
> demonstrations, which will probably be my own failing.
>
> It seems like your main stance is that even if we assume that all votes are
> sincere, we should still have a theory about where the rankings come from, if we
> want to talk about how a method ought to behave.
>
> Maybe this line of thinking can be seen in Yee diagrams, where no strategy is
> considered and methods are judged as to whether win regions match the Voronoi
> diagram.
>
> I may not understand free variables vs. bound variables. It sounds like with
> bound variables, some standard is "right" if it tends to be right. While free
> variables would judge standards to be right or wrong in every specific case.
>
> So you say that a unanimity (or Pareto) criterion would be unjustified under
> free variables with a jury/valence model. While I can see that most standards
> might be unusable with free variables, in the case of unanimity I don't see how
> it could be unjustified. When you discuss IIA it sounds like the jury/valence
> model is essentially an underlying ranking for each voter, with no issue space.
> Is there an assumption that a voter's ranking can be wrong in some sense?
>
> If so, does that also apply to the spatial model? (i.e. that the voter is not
> placed correctly in space.)
>
> I think it's curious that when you bring in "external facts," in both ways
> you've done this, those facts would tell you who the best candidate is in any
> given case. There's no ambiguity. Could we have external facts that don't
> necessarily do this? That wouldn't necessarily be useless, since we could at
> least discuss phenomena in the new terms instead of just on the cast ballots.
>
> What if we think that no model of external facts is justifiable in some
> environment? Can we say nothing then? Maybe our conclusions would reveal some
> implicit assumptions, I suppose, indicating something about what we suspect the
> external facts are.
>
> If the model must tell us the winner (due to one's definition of what a model
> is), I wonder what stops a Condorcet advocate from copy/pasting the cast ballots
> as external facts and declaring that the Condorcet winner within the external
> facts is the targeted, right winner.
>
> When you discuss the validity of Participation under a spatial model, do you
> consider whether the transformations envisioned by the criterion can actually
> be achieved under the model? Perhaps there could be a gray area of satisfaction
> where we say a method fails a criterion, but only if the underlying model is
> wrong (or e.g. if voters are insincere).
>
> I don't understand your criticism of the notion that Participation "relates ...
> to additional incentives offered to voters." Some of us, and Woodall, do
> recognize Participation as a monotonicity criterion, for what it's worth. But I
> don't know how to explain the strategic implications except in terms of
> incentives offered to voters.
>
> When you discuss IIA I am a little confused. You seem very against it, but only
> discuss the jury/valence model. Is it simply obvious that it also applies to the
> spatial model? What you say is that it's "clearly invalid under a Bayesian
> semantics" which seems like an even broader claim.
>
> In order to discuss IRV, you say that if we are willing to accept monotonicity
> as a "valid" criterion under the model, then we can use it to judge the accuracy
> of methods.
>
> I expect there are three possibilities for a proposed criterion and model.
> Either the criterion is valid (i.e. necessarily true), or it's incompatible, or
> it's orthogonal, non-contradictory. In the case of Participation under a spatial
> model, you say this "cannot be valid." I guess you showed it's incompatible.
>
> What do you suppose is the status of a criterion in the middle state, neither
> incompatible nor necessarily true? Must we be indifferent to it, having
> exhausted the only legitimate method of assessing it?
>
> Somewhat related to this, you point out that Borda is ideal or near ideal under
> the jury model. But almost no one actually advocates Borda, for, let's say,
> reasons of strategy. The model can't speak to these reasons, or at least, can't
> ultimately offer us anything but an insistence that we use a Borda-like method.
> I find that disturbing, since the model is what we're using to gauge potential
> properties and that seems like its whole point.
>
> Kristofer mentioned "embarrassment criteria" as an issue. I will often consider
> a criterion important because I think that other people think it's important.
> This results in a lot of subjectivity. For example maybe we can quantify
> monotonicity failure, but how much is too much? Difficult to see a way out of
> this.
>
> Kevin
>
>
> ------------------------------
>
> Message: 2
> Date: Sun, 6 Mar 2022 10:58:33 +0000
> From: Colin Champion <colin.champion at routemaster.app>
> To: EM <election-methods at lists.electorama.com>
> Subject: Re: [EM] Semantics of voting
> Message-ID: <f1cc827d-e770-7a53-83e9-4c3155a99481 at routemaster.app>
> Content-Type: text/plain; charset=utf-8; format=flowed
>
> Kevin - you make a lot of points, I will try to reply to a few of them.
>  ?? I'm sorry if I didn't make myself clear. My own view is that the 
> correctness of electoral decisions needs to be understood evidentially, 
> which in the end means Bayesianly. I am pretty sure that Jack Good held 
> this view and that Kenneth Arrow did not; but when I try to formulate 
> some alternative understanding of the correctness of electoral decisions 
> such as may have been in Arrow's head, I honestly struggle. I cannot be 
> entirely clear about what a non-evidential semantics would look like.
>  ?? I would not say, as a philosophical position, that the semantics 
> need to make reference to a model of voting. If it was possible to put 
> together a model-free formalistic semantics, it might well be 
> acceptable. But in practice I cannot see any viable semantics which does 
> not have a model underlying it. Take this as a challenge, not as a dogma.
>
> My notion of a jury model is that each candidate has an objective 
> valence (or excellence), which we can take to be gaussianly distributed, 
> and that each voter ranks candidates according to his or her own noisy 
> estimates of their valences. This is essentially the model Peyton Young 
> used, except that he worked with probabilities rather than with 
> statistical distributions. (I prefer my own approach because I find it 
> hard to keep a clear head when dealing with probabilities. I'm not sure 
> Young himself entirely succeeded - I think at one point he says 
> "independent" when he means "conditionally independent given... ".)
>
> I'm quite struck by my counterexample to IIA (49% A>C>B, 51% B>A>C, 
> which is simply a numerical version of Good's argument). It seems to me 
> obvious that A is the rightful winner, and that if C is removed from the 
> ballots then B becomes the rightful winner. Certainly anyone who thinks 
> that C simply drops out of the analysis, and that my example is 
> equivalent to 49% A>B, 51% B>A is making an elementary statistical 
> error. I cannot believe that Arrow would have made such a mistake, so I 
> conclude that he understood electoral correctness in a different sense 
> than Good and I do. If only he had told us what it was!
>
> In fact I haven't verified my numbers. Given a little time I could make 
> a plot, similar to the ones on my web page, of isofactors for the pair 
> of fractional ballots 0.49 at A>C>B, 0.51 at B>A>C. I assume there would be a 
> hill whose summit was in the region in which A is better than B and B is 
> better than C. The more ballots you accumulate, the steeper the hill 
> becomes.
>
> Nor have I thought through the application of IIA to spatial models. I 
> don't see any reason why it *should* apply, and maybe Arrow's proof 
> makes it unnecessary to fill in the details. After all, Arrow never 
> limited his theorem to spatial models, and one counterexample is all 
> that's normally called for.
>
> I agree that the Borda count is hopeless in the presence of tactical 
> voting, even under a jury model. But philosophically I don't feel 
> threatened by this. My view is that the right electoral decision is the 
> one which is most likely to give the best candidate, or whose expected 
> loss is least, or whatever, given - simultaneously - a model of sincere 
> voting behaviour and a model of how voters try to beat the system. In 
> practice I recognise that the calculation is beyond anything I can 
> envisage performing, and that even partial results are likely to 
> constitute a significant advance. Under a jury model with tactical 
> voting, I have some evidence that the best methods are the ones with the 
> worst reputations: FPTP and IRV and their extensions (including 
> Condorcet/Hare).
>
> I think my words about the logical criteria may have come across as more 
> dogmatic than I intended. I hadn't realised that participation was 
> sometimes recognised as a form of monotonicity. I think I would say that 
> some criteria are always and necessarily true; some are always or nearly 
> always true, and may may provide useful guidance; and some are totally 
> untrustworthy. So long as one doesn't treat a statistical approximation 
> as a logical truth I have no real complaint.
>
>  ?? Colin
>
>
> ------------------------------
>
> Message: 3
> Date: Sun, 6 Mar 2022 13:41:36 +0000
> From: Colin Champion <colin.champion at routemaster.app>
> To: election-methods at lists.electorama.com
> Subject: [EM] Tactical voting under a jury model
> Message-ID: <71e842ae-4563-ee4d-ec17-6ec84b219b28 at routemaster.app>
> Content-Type: text/plain; charset=utf-8; format=flowed
>
> I wrote in another thread that "under a jury model with tactical voting, 
> I have some evidence that the best methods are the ones with the worst 
> reputations: FPTP and IRV and their extensions". Perhaps some people 
> would like to see the evidence. The following table gives mean valence 
> losses (so smaller is better) under a jury model with voters attempting 
> a burial strategy. It has to be viewed in a fixed-width font.
>
>  ?????????? random?? fptp??? sptp???? av?? sinkhorn borda???? mj coombs
>  ????????? 115.6767? 4.2340 15.4462? 3.4934 22.3533 21.3425??? - 36.3451
>  ???????? condorcet benham?? btr??? nanson minimax minisum??? rp river? 
> schulze?? asm
>  ???????????? -???? 3.5469? 4.6945? 9.5228? 7.7089? 8.0696? 8.4014 
> 8.3864? 9.6397? 9.8513
> condorcet+ random?? fptp??? sptp???? av??? borda
>  ?????????? 9.9406? 4.9425 11.5035? 3.5441 14.2516
>  ?copeland+ random? fptpf?? fptpr??? sptp??? avf???? avr??? bordaf 
> bordar minimaxfminimaxr
>  ????????? 11.4423? 9.6349 10.7388 12.4150? 9.5974 10.5371 14.4200 
> 12.7967? 8.7613 12.0312
>  ??? smith+ random? fptpf?? fptpr??? sptp??? avf???? avr??? bordaf 
> bordar minimaxfminimaxrtideman?? q&dc
>  ?????????? 9.6397? 4.9559? 4.9856 11.5026? 3.5442? 3.5532 14.2516 
> 10.0643? 7.7106? 7.7106? 4.0854? 7.3363
>
> AV (=IRV) seems to be best, while most Condorcet methods do badly and 
> the Borda count does appallingly.
>
> These results are from my own evaluation software; full details are at 
> https://www.masterlyinactivity.com/condorcet/condorcet.html? The call is 
> "condorcet 5 101 100000 jury:2+bur". Obviously the correctness of my 
> code is not guaranteed.
>
> I've never seen an evaluation under a jury model, even assuming sincere 
> voting. I certainly don't rate such models highly, but I think 
> discussions of voting need a model and spatial models aren't the whole 
> truth, so it helps to keep alternatives in mind.
>
> CJC
>
>
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