My web browser doesn't support it. I look forward to reading what you have
so far. The more we can identify what we are trying to do, the better ... a
truly laudable endeavor!

El mar., 1 de mar. de 2022 9:04 a. m., Colin Champion <
colin.champion@routemaster.app> escribió:

Hi Forest and Colin,

Forest, does your browser support this link?
https://www.masterlyinactivity.com/condorcet/semantics.html

Note the difference between "http" (bad old insecure link) and "https"
(secure, encrypted link).  These days, Chrome and other browsers are
starting to require "https", even when you don't care about
security/privacy/etc.

Colin: I suppose that's useful for you to know too, since your website
supports "https" links as a replacement for "http" links.

Rob

Rob

On Tue, Mar 1, 2022 at 4:37 PM Forest Simmons
forest.simmons21@gmail.com wrote:

On 01.03.2022 18:03, Colin Champion wrote:

The closest thing I know of are the frequentist approaches to modeling
election methods, e.g. Kemeny as MLE of a certain extension of the model
in Condorcet's jury theorem, and generalizations to this approach (e.g.
https://www.jstor.org/stable/41106629).

Bayesian statistics is not my field, but as I understand your page,
you're trying to show whether certain models can naturally result in
monotonicity and participation failures, similar to how e.g. IIA by
necessity arises from every ordinal method.

The idea of trying to recover the statistical parameters of issue space
and then electing the best candidate is a good one; I think the reason
there hasn't been much of it is that voting methods research has been
more focused on strategy and on pass-or-fail criteria.

Do there exist extensions to Bayesian stats that handle cases where the
input data may be adversarially corrupted by some party who seeks to
confuse the process? That'd be like voting method strategy.

There's also the issue of noise. In your tetrahedron vs line example,
it's possible that one of the voters filled in the ballot incorrectly
(or misjudged or something). But I imagine that "ordinary" Bayesian
stats could handle noise with appropriately broad priors.

I also think that some properties are considered as "embarrassment
criteria", as in: it seems illogical that a method should fail this
particular criterion, and the opponents of the method might use this to
ridicule the method, so we better patch it up. Or it may be part of how
we think a voting method should behave, no matter what.

Binary properties give a certain guarantee that if something strange
happens, it won't be of this particular type. Let's say, for instance,
that we want to generalize majority rule. And suppose that under a
particular model (jury, say), Borda is optimal. Then if we want to
uphold majority rule no matter what, but still want some performance on
jury models, then Black may be a better choice than Borda.

In a way, there's always a question of what matters.

But looking closely into how VSE might be optimized by Bayesian methods
and how certain spaces imply certain properties is definitely
worthwhile, I think :-)

-km

Hi Colin,

Le mardi 1 mars 2022, 11:04:13 UTC−6, Colin Champion colin.champion@routemaster.app a écrit :

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

On 06.03.2022 14:41, Colin Champion wrote:

That makes sense because FPTP and IRV have in common that burial doesn't
really work: either it does nothing or A>W voters burying W makes
someone else than A win. And it also seems reasonable that the minmax
methods do worse than Condorcet-IRV hybrids since the latter pass DMTBR
and the former don't.

For compromising strategy, I imagine that FPTP and IRV would be
considerably worse than the Condorcet methods.

I suppose you could try Daniel Carrera's trivial strategy, but I'm not
sure how you would translate it into a score. A method is susceptible to
trivial strategy in an election if there exists a candidate X different
from the winner W so that when all the voters who prefer X to W move X
first on their ballots and W last, then X wins.

But if the strategy can be pulled off for more than one X, then what
election counts for calculating the score of the method? I'm not sure.

I'd guess that the trivial strategy would also put the IRV-likes ahead
of (better than) the rest.

What's most surprising, IMHO, is that Condorcet-IRV hybrids do worse
than just plain IRV. James Green-Armytage gives a result where
Condorcetifying a method (electing the CW if there is one) can't
increase the proportion of elections where strategy works, if a majority
can force an outcome for the method in question. But apparently this
does not extend to gracefully degrading: your results seem to show that
even if there are fewer elections where strategy is possible, then under
this model, the strategy does more harm on average where it is possible
to execute.

Some of the columns seem to almost run into each other; perhaps it would
be better to split them over two rows.

That Copeland does so badly also seems to tally well with my own
results. If I'm correct, then Landau should be slightly worse than
Smith, but not anywhere near Copeland.

Are the Smith+ methods Smith// or Smith,?

Another non-spatial/jury-like possibility is the Kemeny model: there's a
distinguished "ground truth" order of the candidates. Each voter casts a
vote according to this ground truth, but for every pairwise preference,
flips them around with some probability p.

So the procedure would be to take the ground truth, and rejection sample
applying the independent noise to the pairwise components, until the
result is transitive (i.e. no voter can cast a cyclical ballot, so just
keep trying until it isn't).

E.g. if the G.T. is A>B>C>D, then a ballot may become
A>B A>C A>D B>C B>D C>D
truth        T  T  T  T  T  T
corrupted    T  F  T  F  T  T

C>A>B>D, instead.

Then the voting method's performance is given by the Kendall tau
distance between the ground truth and the social order produced by the
method when given these ballots.

And if you want to assign scores to impartial culture, then Durand's
hypersphere model might work. I'm not entirely sure how that works (or
how you would sample from it), but Forest showed that it's a natural
extension of impartial culture.

-km

Hi Colin,

Ok. A sort of hidden rating, and the voters use them to populate whichever type
of ballot is provided.

Doesn't IIA hold within a jury model? I mean the estimates of valences.
Perhaps Arrow intends such a model, and means that it would be reasonable to
hope that a property of the model could also be reflected in the procedure.

My view is pretty similar.

Kevin