[EM] Problems with finding the probable best governor

[Blake Cretney]

On Wed, 19 Jul 2000, "MIKE OSSIPOFF" wrote:
> EM list--
> 
> Since the probable-best-government argument is probably used
> as an arguement for Tideman(m), 

I used this argument, so you can take out the "probably".

> I want to point out that
> all that Blake claims for that method is that the margin
> of A's defeat of B is a good measure of the probability that
> A would be a better President than B would--the probability that
> that defeat is "right". As I understand it, then, there's no claim
> that Tideman(w) chooses the candidate who in some way is the
> one who is most likely to be the best President.

Pardon?  What is "Tideman(w)"?  If it's meant to be Tideman(m), then
clearly I claim that very thing.  Whether or not I'm right is
arguable, but I certainly claim it.

> The first thing to point out about that is that Blake is
> apparently assuming that everyone is ranking sincerely.

Yes and no.  It's true that I think it is often useful to ask what
would be the best choice assuming everyone is voting sincerely.  That
doesn't mean that I actually believe that everyone will always rank
sincerely, just that to answer certain questions, one must assume
this, much as economists will use the assumption that everyone
behaves rationally, but are aware that this is not the case.

> But Blake himself has recommended the "general pairwise-count
> defensive strategy" for voters in a Tideman(m) election.

Often buildings have a sign recommending you use the stairs in the
case of fire.  That doesn't mean they actually expect a fire.  They
are just giving a strategy for dealing with it, if it happens.

> Tideman(m), like any margins method, and like any rank-count
> other than Schulze & Condorcet, places on voters a serious need
> for strategic voting. 

I guess that's where we differ in opinion.  I don't expect that
strategy will predominate in Tideman (m).  Certainly, if we expect
that many elections will be decided without strategy, even if these
are in the minority, it is important how they turn out.  BTW, what
method are you calling "Condorcet"?

> And, without sincere voting, the margins of
> defeat in Tideman(m) aren't going to say anything about the
> likelyhood that the defeats are "right", in terms of how likely
> candidate A is to be better than candidate B.

In that case the margin of victory will be partly attributable to the
strategy, and partly attributable to real difference in the ability
of the candidates to atract support.

I'm just amazed that you can see these issues in such black and white
terms.  Obviously we disagree on whether Tideman (m) is more affected
by strategy than Tideman (wv).  But you go further and seem to argue
that Tideman (wv) will be almost unaffected by strategy, while
Tideman (m) is so dominated by strategy that it isn't even worth
while wondering what happens if people in general don't vote
strategically.

I suspect you would view the successive elimination method used in
leadership races in many countries to be very open to strategy. 
Judging by the media coverage of these events, I doubt that more than
a small fraction of voters are aware of potential strategies.

> Even if Blake isn't concerned about need for strategy, it
> still spoils Tideman(w)'s ability to accomplish what Blake would
> like it to accomplish.
>
> Another thing. The goal that Blake discusses is the goal of
> finding the candidate who is the most likely to be the best
> President. But, as I was saying earlier, Tideman(m), even if
> people voted sincerely, and even if probabilities could be
> measured as Blake specifies, wouldn't choose the candidate most
> likely to govern best. The margins of defeat only tell how likely
> each defeat is to be "right". If we want to find out which
> candidate is the most likely to govern best, then we don't want
> to just make pairwise comparisons; we want to add, for each
> candidate, those probabilities, to give each candidate an
> absolute election-wide score. For instance, if the number of
> people ranking A over B measures the probability that A is better
> than B, as is assumed in Blake's justification of Tideman(m), and
> if the number of people ranking B over A similarly counts against
> A's probability of being the best, which is how Vab-Vba is
> justified as the measure of A's probability of being better than B,
> then, if we want to find out A's probability of being the best
> candidate, we need to add up all the individual pair-orderings
> that have A over another candidate, and subtract from that all
> the individual pair-orderings that have another candidate over A.
> In other words, we should count the rankings by Borda's method.

Your conclusion does not follow from your premise.

> Of course Borda has even more problems than Tideman(m), but,
> if we assume sincere voting, and if we want to pick the candidate
> most likely to be the best, based on rankings, then Borda seems
> to be the way to do it, based on the assumptions by which Blake
> justifies margins as a measure of whether a defeat is "right".

You are committing the error of assuming that given proposition A,
and given proposition B such that B implies A, we know B to be true. 
Margins is implied by Borda, not the other way around.

> But, if we can count on voters to be sincere, then need we use
> rankings? Wouldn't it be even better to use a points-assignment
> method? Say people sincerely rate the candidates, and the candidate
> getting the overall most rating points wins.

Sigh.  I guess this means you didn't read any of my exchange on this
topic with Bart.  In fact, I have argued strenuously against this
point.
 
> Obviously that would be no good in public elections if everyone
> isn't voting sincerely. And people won't vote sincerely in
> point-assignment, or Borda, or Tideman(m).

Tideman (m) only differs from Tideman(wv) by allowing voters to leave
candidates unranked as a reasonable option instead of a trap.

> ***
> 
> Average social utility is a measure of something similar to
> Blake's goal.

Similar in what way?

> Maybe the most convincing, for me, explanation of social utility's
> importance is: Say that some new single-winner method will be
> used in some distant election, years down the line. We don't
> know what the candidate lineup will be, what kind of an "example"
> it will be, or which voters we'll be in that example. Obviously
> if that distant election is going to be by a method which we know
> to do well by average social utility, our expectation, estimated
> now,
> for that election's outcome is better than it would be if the
> election were going to use a method which we know to have poorer
> average social utility. So one can tell someone: "No matter which
> method you prefer, no matter whether you value social utility,
> _you_ can expect to be better off if we use the method with
> better average SU".
> 

First of all, there is a distinction between utility, and what I call
normalized utility.  Logically, the possible difference in utility of
various candidates to a voter is unbounded (or at least I can't
imagine how you would arrive at a bound).  However, I suspect that
you are imagining people give candidates a score normalized so that
the least liked candidate is 0 and the most 100.

If so, then clearly this is not a true measure of social utility. 
The outcome of the election could be much more important to one voter
than another.

How closely normalized utility aproximates actual utility seems to me
to be an open question.  There may be methods that aproximate it more
closely, there may not.

Of course, you could have unbounded utilities, but that creates its
own problem.  If you consider yourself a highly emotional person who
sees stark differences between candidates, then you would like this
system, because it exagerates the influence of your vote.  If,
however, you are more measured, and tend to see candidates as
similar, then you could guess ahead of time that social utility would
be bad for you.

In fact, I think that a true social utility measure tends to
exagerate the power of the most irrational voters.  Because I want
rational decisions to be made, I would not assume that I would be
better off under SU.  In fact, I conclude this about Normalized SU
too.

As well, what do you consider a sincere vote?  To me, a sincere vote
is what I consider best.  Like most people, this is probably somewhat
affected by a confusion between what is best for me and what is best
over all.  Nevertheless, people almost always vote the way they think
is best in general, not just for themselves.

But if people voted that way in your suggested election, then since
an individual vote is not a measure of the candidates' utilities to
that voter, even if all perceived utilities were accurate, the total
would not be the true utility of each candidate.

In simpler terms, maximizing satisfaction with the election result is
not the same as maximizing the percieved social utility of the
outcome, because more selfish people will be less satisfied with
benefits going to others than will less selfish people.  So, to
maximize satisfaction, it is necessary to give more benefits to the
selfish, where they cause more satisfaction, even though this may
decrease the overall benefit to society.

This gives another reason to reject SU ahead of time.

---
Blake Cretney