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

[Alex Small]

Forest Simmons said:
> 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.

If you mean the outcome is the same whether people use their optimum
strategies, then it means that there is no incentive to vote insincerely. 
If the method uses ranked ballots then it violates the
Gibbard-Satterthwaite Theorem.

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

> 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.

Well, if it isn't responsive to changes in the electorate, then it isn't
very responsive to the ballots received, be their sincere or insincere.

If we think of an election method as partitioning the space of all
possible electorates into distinct regions corresponding to different
winners, then we might measure manipulability by looking at the shape of
boundaries between regions.  The more the boundary bends and curves, the
more chances for manipulation.  So maybe some sort of geometric or
topological measure of "flatness" or whatever would be useful for
quantifying manipulability.

If we impose the neutrality condition, which is basically a symmetry
condition in the space of all possible electorates, and the anonymity
condition (to reduce the dimensionality of the space from some huge number
depending on the number of voters to some small number depending on the
number of candidates) and the Pareto condition (as a boundary condition)
we could perhaps search for methods that minimize the manipulability.

I'm pretty sure that most proofs of the Gibbard-Satterthwaite Theorem
would show that to minimize manipulability you must elect the Condorcet
Winner when such a candidate exists.




Alex