Problems with finding the probable best governor

[MIKE OSSIPOFF]

EM list--

I accidentally lost my copy of the letter I'm replying to here,
and so I had to copy it from the archives. But it copies here
in a messed-up format. Hopefully it will appear better as e-mail.
If not, sorry about that.


Blake wrote:

[Mike apparently believes that...]

                  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 reply:

It's just that Tideman(m) doesn't offer any of the guarantees
that I want from a single-winner method, in regards to need
for strategy. As Rob pointed out, voters want the best for
themselves, and if truncation is profitable, they'll find out.
And if defensive upranking or defensive order-reversal could
have avoided a very undesirable outcome in an election,
people will notice that too, and then we'll start hearing
advice to vote "pragmatically". We don't need to keep that
situation.

You mentioned newspapers in IRV countries.
I don't know if Australian newspapers have articles advising
lesser-of-2-evils voting, but if they don't, that might merely
reflect a difference in their newspapers from ours. Maybe
U.S. newspapers are taking on more of a social control roll than
Australian papers are. Do British newspapers have articles advising
voters to vote for a lesser-evil instead of a "spoiler"? Of course
Plurality is used there too. I don't think Australian newspapers
can be used to show that IRV or Tideman(m) wouldn't have strategy
problems here.

Blake wrote:


                  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.

I reply:

Whoops--I answered that Australian media question above where
it appears hear, instead of below. Australia is different from
the U.S., and its newspapers might have different goals.
I went into that more above.

Blake wrote:

(that I'd said...)

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.


True. Your pairwise merit comparison estimates don't really
give us something that can be added to get an overall score
for a candidate. But still, without saying that Tideman(m)
implies it, it seems reasonable to say that, by counting how
many individual pairwise preference votes have X over another
candidate, we could estimate how good X is. But I shouldn't say
that that should replace Tideman(m) or that Tideman(m) implies
it. Anyway, I wouldn't use that Borda count because people don't
vote sincerely with methods like that.

But I don't understand how Tideman(m) estimates the best
candidate. It locks in large-margin defeats, by skipping as
low in the margin-strength-ordered defeat list as possible, but
when that makes a transitive sequence of defeats, what makes the
candidate at the top of that transitive candidate ordering more
likely to be the best than some candidate in the middle of
the ordering? Maybe he lost pairwise to that candidate.
In that case, all you have to
claim that the candidate at the top of the ordering is more likely
to be the best than someone in the middle of the ordering is
the assumption that the probabilities that you estimate from the
margins are related transitively.

So it seems to me that Borda, which estimates a candidate's merit
from how many individual pairwise preference votes have him over
someone else, has at least as good a claim to validity as
Tideman(m), as an estimate of which candidate is the best.

Which is more questionable: Assuming that the pairwise probabilities
estimated from  certain of the pairwise margins are transitive, &
ignoring thatthe top candidate was defeated (the people indicated that
else was better than he is), or counting a candidate's favorable
individual pairwise preference votes as a measure of how likely
he is to be the best candidate? The latter approach doesn't
interpret (the conflicting) pairwise defeats as saying anything
about likelihood of being the best candidate. It says that each
individual favorable pairwise preference vote counts as evidence
for how likely that candidate is to be the best one.

So isn't there a good case for saying that Borda's estimate
of the candidate most likely to be the best doesn't involve
as doubtful assumptions as Tideman(m)'s estimate? The pairwise
defeats contradict eachother. An individual's pairwise preference
votes don't contradict eachother. Borda merely adds those up
for each candidate.

For anyone who doesn't know me, I want to re-emphasize that I
don'r recommend Borda, which has serious problems that disqualify
it in the opinion of many, including me.


                 > 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".

Again, Blake was correct that I can't justify Borda in terms
of Tideman(m).



                  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.

Ok, but now I'm just comparing the 2 methods without basing
either on the other.


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.

I reply:

True, wasn't following that discussion, because at that time
I didn't realize why SU matters so much. Of course I should have
checked the archives to find out what was said, before writing.

Blake wrote:


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


Though standards are an individual subjective matter of opinion,
and Tideman(m) vs Borda could be considered a matter of opinion,
I say that the above statement is just incorrect.

Tideman(wv) doesn't trap you if you truncate. Admittedly, with
_any_ method, if the people who need a compromise don't support that
compromise, then they suffer as a result. But if the people who
don't need a middle compromise candidate refuse to vote for him,
Tideman(wv) doesn't do anything to make them regret that. It
merely is unaffected by that truncation. Saying that truncation
is a trap in Tideman(wv) implies that voters suffer from truncation
more with Tideman(wv) than with Tideman(m). Not so.

The real difference between Tideman(m) & Tideman(wv) is that
Tideman(wv) doesn't let truncation cause a violation of majority
rule. That means that Tideman(wv), unlike Tideman(m), doesn't
create a situation where a majority has to use some drastic
strategy to get its due. That's why majority rule and the need
for defensive strategy are related.

I believe that most would agree with me that majority rule and
getting rid of the lesser-of-2-evils problem are more important,
even though, as I said, standards are a subjective individual
matter of opinion.


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

Blake asked:


                  Similar in what way?


I reply:

You're interested in estimating which candidate would bring
the best government. SU is an estimate of that too. Both
estimates are based on some sort of aggregation of of some
indication of how individual voters feel about the candidates.

If maximizing SU means that the people are most pleased overall,
isn't that a lot like best government?


Blake pointed out the difference between utility & normalized
utility, and pointed out that that causes a problem when using
Points-Assignment to try to maximize SU. What he says is true.
Blake, in fact, in this letter, points out several problems with
using Points-Assignment to try to maximize SU, and those problems,
some of which hadn't occurred to me, all seem valid. Of course
that doesn't mean that Points-Assignment (with voters who
are sincere about what's best for them) wouldn't do better at
SU than Tideman(m) does.

As Blake suggests, the only way of doing Points-Assignment that
wouldn't violate Anonymity would be to limit the maximum &
minimum assignments..


Blake wrote:

   In fact, I think that a true social utility measure tends to
                  exagerate the power of the most irrational voters.

Because irrational voters vote in extreme ways? I don't know
that they do. Right now, millions of very irrational voters are
voting conservatively, and the ones who vote for someone
extreme (genuinely different), and vote for Nader, are the
rational ones. So I don't think it's fair to say that extreme
voters are more likely to be irrational.



                  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 objection is easily answered. These entirely honest voters
are instucted to rate the candidates (or alternatives) according
to their own estimated benefit from the candidates or alternatives.
That's how I'd conduct Points-Assignment, if the voters were
honest enough to use it. That way the more selfish voters wouldn't
have any advantage.

Again, though, I don't recommend Points-Assignment for our
public political elections.

Mike Ossipoff



________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com