<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
</head>
<body>
<div><div>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:<br><br></div><div><a href="https://en.wikipedia.org/wiki/Spatial_model_of_voting#Accuracy" rel="noopener noreferrer" target="_blank">https://en.wikipedia.org/wiki/Spatial_model_of_voting#Accuracy</a><br></div><br>I think there's some good support there for the spatial model.<br><br>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:<br><br></div><div><a href="https://votevote.page/">https://votevote.page/</a><br></div><div><br>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).</div><div><br></div><div>Mar 6, 2022, 1:02 PM by election-methods-request@lists.electorama.com:<br></div><blockquote class="tutanota_quote" style="border-left: 1px solid #93A3B8; padding-left: 10px; margin-left: 5px;"><div>Send Election-Methods mailing list submissions to<br></div><div> election-methods@lists.electorama.com<br></div><div><br></div><div>To subscribe or unsubscribe via the World Wide Web, visit<br></div><div> http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com<br></div><div><br></div><div>or, via email, send a message with subject or body 'help' to<br></div><div> election-methods-request@lists.electorama.com<br></div><div><br></div><div>You can reach the person managing the list at<br></div><div> election-methods-owner@lists.electorama.com<br></div><div><br></div><div>When replying, please edit your Subject line so it is more specific<br></div><div>than "Re: Contents of Election-Methods digest..."<br></div><div><br></div><div><br></div><div>Today's Topics:<br></div><div><br></div><div> 1. Re: Semantics of voting (Kevin Venzke)<br></div><div> 2. Re: Semantics of voting (Colin Champion)<br></div><div> 3. Tactical voting under a jury model (Colin Champion)<br></div><div><br></div><div><br></div><div>----------------------------------------------------------------------<br></div><div><br></div><div>Message: 1<br></div><div>Date: Sun, 6 Mar 2022 05:56:13 +0000 (UTC)<br></div><div>From: Kevin Venzke <stepjak@yahoo.fr><br></div><div>To: EM <election-methods@lists.electorama.com>, Colin Champion<br></div><div> <colin.champion@routemaster.app><br></div><div>Subject: Re: [EM] Semantics of voting<br></div><div>Message-ID: <1465719469.329608.1646546173987@mail.yahoo.com><br></div><div>Content-Type: text/plain; charset=UTF-8<br></div><div><br></div><div>Hi Colin,<br></div><div><br></div><div>Le mardi 1 mars 2022, 11:04:13 UTC?6, Colin Champion <colin.champion@routemaster.app> a ?crit : <br></div><blockquote><div>I started drafting a post on this subject, but it got longer and longer <br></div><div>so I turned it into a web page: <br></div><div>http://www.masterlyinactivity.com/condorcet/semantics.html<br></div></blockquote><div>>? ? Briefly, I argue that discussions of voting methods are only <br></div><div>>?meaningful if a semantics can be attached to the correctness of <br></div><div>>?electoral decisions; that models (such as jury and spatial models) can <br></div><div>>?provide such a semantics, leading to a Bayesian interpretation of <br></div><div>>?correctness; that the logical criteria stand or fall according to <br></div><div>>?whether they can be validated under a suitable semantics; that some <br></div><div>>?stand, some fall, and some are best seen as statistical approximations.<br></div><div><br></div><div>>??? The topics I discuss are ones I have not seen addressed elsewhere. I <br></div><div>>?have no idea how new my ideas are, or whether, if I was better grounded <br></div><div>>?in the field, I'd have been able to discuss the subject with greater wisdom.<br></div><div><br></div><div>I read through this a few times. I think I understand most of it, other than the<br></div><div>demonstrations, which will probably be my own failing.<br></div><div><br></div><div>It seems like your main stance is that even if we assume that all votes are<br></div><div>sincere, we should still have a theory about where the rankings come from, if we<br></div><div>want to talk about how a method ought to behave.<br></div><div><br></div><div>Maybe this line of thinking can be seen in Yee diagrams, where no strategy is<br></div><div>considered and methods are judged as to whether win regions match the Voronoi<br></div><div>diagram.<br></div><div><br></div><div>I may not understand free variables vs. bound variables. It sounds like with<br></div><div>bound variables, some standard is "right" if it tends to be right. While free<br></div><div>variables would judge standards to be right or wrong in every specific case.<br></div><div><br></div><div>So you say that a unanimity (or Pareto) criterion would be unjustified under<br></div><div>free variables with a jury/valence model. While I can see that most standards<br></div><div>might be unusable with free variables, in the case of unanimity I don't see how<br></div><div>it could be unjustified. When you discuss IIA it sounds like the jury/valence<br></div><div>model is essentially an underlying ranking for each voter, with no issue space.<br></div><div>Is there an assumption that a voter's ranking can be wrong in some sense?<br></div><div><br></div><div>If so, does that also apply to the spatial model? (i.e. that the voter is not<br></div><div>placed correctly in space.)<br></div><div><br></div><div>I think it's curious that when you bring in "external facts," in both ways<br></div><div>you've done this, those facts would tell you who the best candidate is in any<br></div><div>given case. There's no ambiguity. Could we have external facts that don't<br></div><div>necessarily do this? That wouldn't necessarily be useless, since we could at<br></div><div>least discuss phenomena in the new terms instead of just on the cast ballots.<br></div><div><br></div><div>What if we think that no model of external facts is justifiable in some<br></div><div>environment? Can we say nothing then? Maybe our conclusions would reveal some<br></div><div>implicit assumptions, I suppose, indicating something about what we suspect the<br></div><div>external facts are.<br></div><div><br></div><div>If the model must tell us the winner (due to one's definition of what a model<br></div><div>is), I wonder what stops a Condorcet advocate from copy/pasting the cast ballots<br></div><div>as external facts and declaring that the Condorcet winner within the external<br></div><div>facts is the targeted, right winner.<br></div><div><br></div><div>When you discuss the validity of Participation under a spatial model, do you<br></div><div>consider whether the transformations envisioned by the criterion can actually<br></div><div>be achieved under the model? Perhaps there could be a gray area of satisfaction<br></div><div>where we say a method fails a criterion, but only if the underlying model is<br></div><div>wrong (or e.g. if voters are insincere).<br></div><div><br></div><div>I don't understand your criticism of the notion that Participation "relates ...<br></div><div>to additional incentives offered to voters." Some of us, and Woodall, do<br></div><div>recognize Participation as a monotonicity criterion, for what it's worth. But I<br></div><div>don't know how to explain the strategic implications except in terms of<br></div><div>incentives offered to voters.<br></div><div><br></div><div>When you discuss IIA I am a little confused. You seem very against it, but only<br></div><div>discuss the jury/valence model. Is it simply obvious that it also applies to the<br></div><div>spatial model? What you say is that it's "clearly invalid under a Bayesian<br></div><div>semantics" which seems like an even broader claim.<br></div><div><br></div><div>In order to discuss IRV, you say that if we are willing to accept monotonicity<br></div><div>as a "valid" criterion under the model, then we can use it to judge the accuracy<br></div><div>of methods.<br></div><div><br></div><div>I expect there are three possibilities for a proposed criterion and model.<br></div><div>Either the criterion is valid (i.e. necessarily true), or it's incompatible, or<br></div><div>it's orthogonal, non-contradictory. In the case of Participation under a spatial<br></div><div>model, you say this "cannot be valid." I guess you showed it's incompatible.<br></div><div><br></div><div>What do you suppose is the status of a criterion in the middle state, neither<br></div><div>incompatible nor necessarily true? Must we be indifferent to it, having<br></div><div>exhausted the only legitimate method of assessing it?<br></div><div><br></div><div>Somewhat related to this, you point out that Borda is ideal or near ideal under<br></div><div>the jury model. But almost no one actually advocates Borda, for, let's say,<br></div><div>reasons of strategy. The model can't speak to these reasons, or at least, can't<br></div><div>ultimately offer us anything but an insistence that we use a Borda-like method.<br></div><div>I find that disturbing, since the model is what we're using to gauge potential<br></div><div>properties and that seems like its whole point.<br></div><div><br></div><div>Kristofer mentioned "embarrassment criteria" as an issue. I will often consider<br></div><div>a criterion important because I think that other people think it's important.<br></div><div>This results in a lot of subjectivity. For example maybe we can quantify<br></div><div>monotonicity failure, but how much is too much? Difficult to see a way out of<br></div><div>this.<br></div><div><br></div><div>Kevin<br></div><div><br></div><div><br></div><div>------------------------------<br></div><div><br></div><div>Message: 2<br></div><div>Date: Sun, 6 Mar 2022 10:58:33 +0000<br></div><div>From: Colin Champion <colin.champion@routemaster.app><br></div><div>To: EM <election-methods@lists.electorama.com><br></div><div>Subject: Re: [EM] Semantics of voting<br></div><div>Message-ID: <f1cc827d-e770-7a53-83e9-4c3155a99481@routemaster.app><br></div><div>Content-Type: text/plain; charset=utf-8; format=flowed<br></div><div><br></div><div>Kevin - you make a lot of points, I will try to reply to a few of them.<br></div><div> ?? I'm sorry if I didn't make myself clear. My own view is that the <br></div><div>correctness of electoral decisions needs to be understood evidentially, <br></div><div>which in the end means Bayesianly. I am pretty sure that Jack Good held <br></div><div>this view and that Kenneth Arrow did not; but when I try to formulate <br></div><div>some alternative understanding of the correctness of electoral decisions <br></div><div>such as may have been in Arrow's head, I honestly struggle. I cannot be <br></div><div>entirely clear about what a non-evidential semantics would look like.<br></div><div> ?? I would not say, as a philosophical position, that the semantics <br></div><div>need to make reference to a model of voting. If it was possible to put <br></div><div>together a model-free formalistic semantics, it might well be <br></div><div>acceptable. But in practice I cannot see any viable semantics which does <br></div><div>not have a model underlying it. Take this as a challenge, not as a dogma.<br></div><div><br></div><div>My notion of a jury model is that each candidate has an objective <br></div><div>valence (or excellence), which we can take to be gaussianly distributed, <br></div><div>and that each voter ranks candidates according to his or her own noisy <br></div><div>estimates of their valences. This is essentially the model Peyton Young <br></div><div>used, except that he worked with probabilities rather than with <br></div><div>statistical distributions. (I prefer my own approach because I find it <br></div><div>hard to keep a clear head when dealing with probabilities. I'm not sure <br></div><div>Young himself entirely succeeded - I think at one point he says <br></div><div>"independent" when he means "conditionally independent given... ".)<br></div><div><br></div><div>I'm quite struck by my counterexample to IIA (49% A>C>B, 51% B>A>C, <br></div><div>which is simply a numerical version of Good's argument). It seems to me <br></div><div>obvious that A is the rightful winner, and that if C is removed from the <br></div><div>ballots then B becomes the rightful winner. Certainly anyone who thinks <br></div><div>that C simply drops out of the analysis, and that my example is <br></div><div>equivalent to 49% A>B, 51% B>A is making an elementary statistical <br></div><div>error. I cannot believe that Arrow would have made such a mistake, so I <br></div><div>conclude that he understood electoral correctness in a different sense <br></div><div>than Good and I do. If only he had told us what it was!<br></div><div><br></div><div>In fact I haven't verified my numbers. Given a little time I could make <br></div><div>a plot, similar to the ones on my web page, of isofactors for the pair <br></div><div>of fractional ballots 0.49@A>C>B, 0.51@B>A>C. I assume there would be a <br></div><div>hill whose summit was in the region in which A is better than B and B is <br></div><div>better than C. The more ballots you accumulate, the steeper the hill <br></div><div>becomes.<br></div><div><br></div><div>Nor have I thought through the application of IIA to spatial models. I <br></div><div>don't see any reason why it *should* apply, and maybe Arrow's proof <br></div><div>makes it unnecessary to fill in the details. After all, Arrow never <br></div><div>limited his theorem to spatial models, and one counterexample is all <br></div><div>that's normally called for.<br></div><div><br></div><div>I agree that the Borda count is hopeless in the presence of tactical <br></div><div>voting, even under a jury model. But philosophically I don't feel <br></div><div>threatened by this. My view is that the right electoral decision is the <br></div><div>one which is most likely to give the best candidate, or whose expected <br></div><div>loss is least, or whatever, given - simultaneously - a model of sincere <br></div><div>voting behaviour and a model of how voters try to beat the system. In <br></div><div>practice I recognise that the calculation is beyond anything I can <br></div><div>envisage performing, and that even partial results are likely to <br></div><div>constitute a significant advance. Under a jury model with tactical <br></div><div>voting, I have some evidence that the best methods are the ones with the <br></div><div>worst reputations: FPTP and IRV and their extensions (including <br></div><div>Condorcet/Hare).<br></div><div><br></div><div>I think my words about the logical criteria may have come across as more <br></div><div>dogmatic than I intended. I hadn't realised that participation was <br></div><div>sometimes recognised as a form of monotonicity. I think I would say that <br></div><div>some criteria are always and necessarily true; some are always or nearly <br></div><div>always true, and may may provide useful guidance; and some are totally <br></div><div>untrustworthy. So long as one doesn't treat a statistical approximation <br></div><div>as a logical truth I have no real complaint.<br></div><div><br></div><div> ?? Colin<br></div><div><br></div><div><br></div><div>------------------------------<br></div><div><br></div><div>Message: 3<br></div><div>Date: Sun, 6 Mar 2022 13:41:36 +0000<br></div><div>From: Colin Champion <colin.champion@routemaster.app><br></div><div>To: election-methods@lists.electorama.com<br></div><div>Subject: [EM] Tactical voting under a jury model<br></div><div>Message-ID: <71e842ae-4563-ee4d-ec17-6ec84b219b28@routemaster.app><br></div><div>Content-Type: text/plain; charset=utf-8; format=flowed<br></div><div><br></div><div>I wrote in another thread that "under a jury model with tactical voting, <br></div><div>I have some evidence that the best methods are the ones with the worst <br></div><div>reputations: FPTP and IRV and their extensions". Perhaps some people <br></div><div>would like to see the evidence. The following table gives mean valence <br></div><div>losses (so smaller is better) under a jury model with voters attempting <br></div><div>a burial strategy. It has to be viewed in a fixed-width font.<br></div><div><br></div><div> ?????????? random?? fptp??? sptp???? av?? sinkhorn borda???? mj coombs<br></div><div> ????????? 115.6767? 4.2340 15.4462? 3.4934 22.3533 21.3425??? - 36.3451<br></div><div> ???????? condorcet benham?? btr??? nanson minimax minisum??? rp river? <br></div><div>schulze?? asm<br></div><div> ???????????? -???? 3.5469? 4.6945? 9.5228? 7.7089? 8.0696? 8.4014 <br></div><div>8.3864? 9.6397? 9.8513<br></div><div>condorcet+ random?? fptp??? sptp???? av??? borda<br></div><div> ?????????? 9.9406? 4.9425 11.5035? 3.5441 14.2516<br></div><div> ?copeland+ random? fptpf?? fptpr??? sptp??? avf???? avr??? bordaf <br></div><div>bordar minimaxfminimaxr<br></div><div> ????????? 11.4423? 9.6349 10.7388 12.4150? 9.5974 10.5371 14.4200 <br></div><div>12.7967? 8.7613 12.0312<br></div><div> ??? smith+ random? fptpf?? fptpr??? sptp??? avf???? avr??? bordaf <br></div><div>bordar minimaxfminimaxrtideman?? q&dc<br></div><div> ?????????? 9.6397? 4.9559? 4.9856 11.5026? 3.5442? 3.5532 14.2516 <br></div><div>10.0643? 7.7106? 7.7106? 4.0854? 7.3363<br></div><div><br></div><div>AV (=IRV) seems to be best, while most Condorcet methods do badly and <br></div><div>the Borda count does appallingly.<br></div><div><br></div><div>These results are from my own evaluation software; full details are at <br></div><div>https://www.masterlyinactivity.com/condorcet/condorcet.html? The call is <br></div><div>"condorcet 5 101 100000 jury:2+bur". Obviously the correctness of my <br></div><div>code is not guaranteed.<br></div><div><br></div><div>I've never seen an evaluation under a jury model, even assuming sincere <br></div><div>voting. I certainly don't rate such models highly, but I think <br></div><div>discussions of voting need a model and spatial models aren't the whole <br></div><div>truth, so it helps to keep alternatives in mind.<br></div><div><br></div><div>CJC<br></div><div><br></div><div><br></div><div>------------------------------<br></div><div><br></div><div>Subject: Digest Footer<br></div><div><br></div><div>_______________________________________________<br></div><div>Election-Methods mailing list<br></div><div>Election-Methods@lists.electorama.com<br></div><div>http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com<br></div><div><br></div><div><br></div><div>------------------------------<br></div><div><br></div><div>End of Election-Methods Digest, Vol 212, Issue 9<br></div><div>************************************************<br></div></blockquote><div dir="auto"><br></div> </body>
</html>