[EM] Myerson's Please-Everyone-Candidate Study
nkklrp at hotmail.com
Sat Nov 20 18:13:20 PST 2004
Regarding James C.'s claim that Approval will cause candidates to pander to
more voters than IRV will, Roger Myerson undertook a study of how various
votiing systems do in that regard.
He proposed an election in which the govt has a certain amount of money to
be divided among the voters. Each candidate has his own proposal for how
that money is to be divided among the voters. Each candidate makes his
offer, his promise to the voters about how he'll divide the money if he
wins. It's assumed that people believe him :-) Ok, maybe candidate campain
promises are unreliable, but most voters seem to believe them, and so let's
disregard that one challengable issue.
He studied a number of voting systems. He found that IRV gives candidates
much more incentive to spread their offers thinly & widely, trying to appeal
to everyone, as compared to Approval.
That isn't surprising. It costs a lot to get someone's Approval vote. The
candidate has to be so good, his offer so great, that the voter is willing
to vote him equal to that voter's favorite. Trying to buy more than a few
voters therefore wouldn't be feasible. In IRV, it's easier to get support
from more voters, since all you need is for them to rank you somewhere
reasonably high, or at least not too low. Pander to lots of them, and be
But I still like Condorcet best. I don't think Condorcet would cause Nader
to pander to Kerry-voter types in order to get them to rank him well. Nader
is anything but a panderer. He wouldn't sell himself to the Kerry voters
with Condorcet any more than he would with Approval or Plurality.
But Myerson's study shows that IRV gives much more incentive for
noncommittal, please-everyone pandering than Approval does.
Check out the article. First, get the _Journal of Economic Perspective_ for
Winter '85. It's a special issue on voting systems. It has an article by
Robert Weber, entitled "Approval Voting". The references at the end of that
article describe a number of interesting, important articles, by Myerson,
and by Mylerson & Weber.
One of those articles is about the exstent to which various voting systems
give candidates incentive to please everyone. That of course is the one that
I'm telling about here. Of course the reference will telll you what issue of
what journal that article is in. Maybe someone on this mailing list can tell
you directly what journal that is, and which issue of that journal. If not,
you can find it via _Journal of Economic Perspective_, as I described.
That references section also has an article by Mylerson about Myerson's
corruption test. He compared varioius methods in a model that studied how
the methods reward or reject corruption.
In that test model, for simplicity, there's a Yes/No issue on which the
various candidates have positions. For a particular voter, a candidate has
(dis)utility depending on which position he holds on that Yes/No issue. But,
a candidate may also have a nonpositional disutility that's the same for
every voter, regardless of that voter's preference on the Yes/No issue. That
Actually, of course, corruption affects issue positions, and so it can't
really be separatred from them. But there's stil something to it of value
The studly showed that Approval will quickly drive corruption from the
political system. But that couldn't be said of Plurality. And Borda rewarded
and preserved corruption in a way that even Plurailty didn't do. Check out
that interesting article.
There's also a reference to an article by Myerson & Weber about a new kind
of voting equilibrium that they propose. Put briefly, a Mlyerson-Weber
equilibrium is an outcome that doesn't contradict the predictive beliefs
that led people to vote in the way that brought about that outcome. Their
actual definition is longer than that, but is interesting & elegant. It only
applies to "positional" methods such as Approval, Plurality, CR, & Borda.
They show that, with Plurality, almost _any_ two parties can keep being "the
2 only viable parties" at Myerson-Weber equilibrium. The media tell us that
they're "The Two Choices", we believe it, we therefore vote for one of
them...and guess what: The winner always comes from that pair. Amazing :-)
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