[EM] Strategy-free Condorcet resolution methods

[Alex Small]

Originally I only sent this to Kevin, when I meant to send it to the whole
list.  Then I realized that he was only asking which methods are _most_
free of incentives for insincere ranking, not which methods are completely
free of incentives for insincere ranking.  Still, I like the little
argument I give here concerning the Gibbard-Satterthwaite Theorem, so I'm
reproducing it for the list.  Here's my original reply to Kevin's message:

Kevin Venzke said:
> Could I get some opinions on what resolution methods
> are most free of incentive to rank insincerely,

There are no such methods.  This was rigorously proven by Gibbard and
Satterthwaite.  In fact, the need for a Condorcet resolution method in
the presence of cycles is precisely why there are incentives to rank
insincerely.

Suppose that we have a Condorcet Winner, and then we only consider
strategic adjustments that change the outcome but still leave a
Condorcet winner (i.e. the adjustments do NOT create a cycle, which then
forces us to resort to a resolution method).  Who would have an
incentive to make such an adjustment?

Say that the candidate who comes in Nth place on your list is the one
who wins all pairwise contests.  There are N-1 candidates whom you'd
prefer to him.  A necessary (but not sufficient) condition for one of
those N-1 candidates to win after you make your adjustment is that you
cause one of those N-1 candidates to defeat candidate N pairwise.  Well,
you've already ranked those N-1 candidates ahead of your the Nth
candidate on your list.  There's nothing more you can do to to help one
of them defeat him
pairwise.

If, however, you could create a cycle with your strategic adjustment,
then maybe one of the N-1 candidates whom you prefer to candidate N
would now win.  So, if there is any incentive to vote insincerely when
there is a Condorcet winner, it must be an incentive to create a cycle.
And since we know that all non-dictatorial and pareto efficient ranked
methods give incentives to vote insincerely, we can say that there will
be cases when voters have incentives to create a cycle.

So, in some sense, the fact that cycles are possible is the reason why
the Gibbard-Satterthwaite Theorem is valid.  If cycles were never
possible, then the Condorcet method would be non-manipulable.

> or run clones, even if the results are "inferior"?

You'll have to ask somebody else about clones.



Alex Small