Re: [EM] Semantics of voting
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:
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@lists.electorama.com:
Send Election-Methods mailing list submissions to
election-methods@lists.electorama.com
To subscribe or unsubscribe via the World Wide Web, visit
http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
or, via email, send a message with subject or body 'help' to
election-methods-request@lists.electorama.com
You can reach the person managing the list at
election-methods-owner@lists.electorama.com
When replying, please edit your Subject line so it is more specific
than "Re: Contents of Election-Methods digest..."
Today's Topics:
- Re: Semantics of voting (Kevin Venzke)
- Re: Semantics of voting (Colin Champion)
- Tactical voting under a jury model (Colin Champion)
Message: 1
Date: Sun, 6 Mar 2022 05:56:13 +0000 (UTC)
From: Kevin Venzke stepjak@yahoo.fr
To: EM election-methods@lists.electorama.com, Colin Champion
colin.champion@routemaster.app
Subject: Re: [EM] Semantics of voting
Message-ID: 1465719469.329608.1646546173987@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@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@routemaster.app
To: EM election-methods@lists.electorama.com
Subject: Re: [EM] Semantics of voting
Message-ID: f1cc827d-e770-7a53-83e9-4c3155a99481@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@A>C>B, 0.51@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@routemaster.app
To: election-methods@lists.electorama.com
Subject: [EM] Tactical voting under a jury model
Message-ID: 71e842ae-4563-ee4d-ec17-6ec84b219b28@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
Subject: Digest Footer
Election-Methods mailing list
Election-Methods@lists.electorama.com
http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
End of Election-Methods Digest, Vol 212, Issue 9