[EM] serious strategy problem in Condorcet, but not in IRV?

[Forest Simmons]

On Tue, 19 Aug 2003, Eric Gorr wrote:

> The only rational choice a rational voter can therefore make is to
> put into place a method which can find the correct winner, based on
> sincere votes, and to vote sincerely.

This idea is interesting to think about:

Suppose for a minute that there is a "correct winner" for each election,
and that you have a method M1 that picks the correct winner when the
voters vote sincerely, but doesn't always do so when the voters use their
optimal strategies.

Suppose also that there is another method M2 that picks the correct winner
in both cases, sincere and strategic.

Since M1 and M2 have no way of knowing if the ballots are sincere or not,
they both pick the winner on the assumption that the ballots are sincere,
and since they both give the same answer (the correct answer) for sincere
ballots, they must agree.

M1 and M2 cannot really give different results in the two cases after all.

This leaves us with four possibilities:

(1) A method that always picks the correct winner with sincere ballots,
also always picks the correct winner when optimal strategies are used by
the voters.

(2) Every method that always picks the correct winner with sincere ballots
fails to pick the correct winner in some cases of strategic ballots.

(3) There is no such thing as a method that always picks the correct
winner for sincere ballots.

(4) "Correct winner" is too fuzzy of a concept to be of much use.


I think we can rule out (1), and that the remaining possibilities are in
order of increasing likelihood.

Here's the most interesting question for me:

Is it possible that increasing resistance to manipulation requires a
sacrifice in the performance of the method in the zero information case?

In other words, manipulation resistance requires a thick skin that puts a
limit on the possible sensitivity and responsiveness of the method to
sincere ballots.

I'm not sure, but I wouldn't be surprised if there were some tradeoff like
this ... a kind of uncertainty principle.

If so, Eric's suggestion above would be one of the two extremes.  At the
other extreme we might try to find a method completely resistant to
strategic manipulation and hope that it doesn't work too badly in the zero
info case.

I think that if you had to pick one extreme over the other, I would take
Eric's.  But perhaps there is a compromise method that is robust enough to
eliminate most of the manipulation and still do pretty good in the zero
information case.

Recently I have suggested some methods that separate the strategic and
sincere parts of the ballots.  The strategic part openly invites strategy
for picking a finalist pair. The sincere part (having nothing to do with
the choice of the finalist pair) elicits the sincere preferences of the
voters to determine which of the two finalists will win the election.

Voters without the interest or patience for participation in the strategic
part can refrain from marking that part without spoiling their ballots.

The strategic part can be any election method applied to pairs of
candidates, i.e. the alternatives to choose from in the strategic part are
pairs of the candidates who are running (individually) in the actual
election.

If the strategic part uses a method that satisfies the weak Favorite
Betrayal Criterion, then the method as a whole satisfies the strong FBC;
since the sincere part of the ballot is not merely expressive; every
sincere preference has some chance of being pivotal.

Any other thoughts along these lines?

Forest