[EM] extending Myerson's test--more policy positions

[MIKE OSSIPOFF]

EM list--

First I want to correct a small typo: When I used the expression
"issue position", I meant "policy position". A policy can be
about a number of issues.

Before I go on, let me tell where to find Myerson's article.

"Effectiveness of Electoral Systems for Reducing Government
Corruption", _Games & Economic Behavior_ 5. (That's number 5,
or, more likely, volume 5. Maybe the volumes aren't divided into
numbers). Pages 118-132.

Myerson also briefly introduces that subject in his article
in the _Journal of Economic Perspective_, Winter '95.

***

If someone asked exactly what I meant by the word "situation",
I'd evade by referring them to Myerson's article. For the purpose
of my discussion about Approval & IRV with more than 2 policy
positions, it doesn't matter, because complete effectiveness
can be worded as "There can't be a Nash equilibrium in which
a corrupt candidate wins." As I was saying before, IRV's failure
is convincing even though it isn't really a Nash equilibrium.

***

I don't have a copy of the article, and that's the only reason
why I don't give the details of Borda's failure described in the
article.

***

But I should justify my statements about Approval & IRV with
more than 2 policy positions, since the article doesn't cover
situations with more than 2 policy positions.

It's sometimes said that, with Approval, if you vote for someone,
it's to your advantage to vote for everyone whom you like more.
I make that suggestion whenever I talk about Approval strategy:
"Vote for the lesser-evil you'd vote for in Plurality, and for
everyone whom you like more."

But, if frontrunner probabilities can take on any values at all,
it isn't strictly true that it's always to your advantage to vote
for everyone whom you like better than someone else for whom
you've voted. There can be situations where your best strategy
instead involves "skipping". I said yesterday that at least one
author said that the combinations of frontrunner probabilities
creating that situation are so unreasonable that the possibility
should be ignored, or might as well be ignored, for strategy
purposes. I don't have a copy of it, so I can't quote his exact
words here. If you want to find out who said that, and exactly
how he worded it, it's probably in Weber's article, "Approval
Voting", in the abovementioned issue of _Journal of Economic
Perspective_. In the unlikely event that it isn't in his article,
it could be in Myerson's article.

It can be shown that if each candidate is assigned his "individual
frontrunner probability", his probability of being one of the
2 frontrunners, and if the frontrunner probability of a pair is
gotten as the product of the 2 candidates' individual frontrunner
probabilities, then maximization of utility expectation always
means that if we vote for someone we vote for everyone whom we
like more. Several authors consider the individual frontrunner
approach a reasonable thing to use, and suggest it for calculating
strategy.

Now, if we accept that we should vote for everyone whom we like
better than Joe, if we vote for Joe, then everyone voting for
a corrupt candidate improves his utility expectation if he also
votes for that candidate's uncorrupt counterpart at the same
policy position. Even if everyone at that policy position voted
for the corrupt one, he does better, expectationwise, if he also
votes for that candidate's uncorrupt counterpart. Then the best
that the corrupt candidate can do is tie with his uncorrupt
counterpart. So a clear victory for that corrupt candidate
won't happen if each voter who helps him changes his strategy
in a way that would improve his expectation even if the change
were unilateral.

***

I'd better send this, and then send the IRV part immediately
subsequently.

Mike Ossipoff

______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com