[EM] Defensive strategy for Condorcet methods KM

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Hi Kristofer,
> 
> --- En date de : Lun 13.6.11, Kristofer Munsterhjelm <km_elmet at lavabit.com> a écrit :
>> If you want something that deters burial strategy, how
>> about what I called FPC? Each candidate's penalty is equal
>> to the number of first-place votes for those who beat him
>> pairwise. Lowest penalty wins.
>> Burying a candidate may help in engineering a cycle, but it
>> can't stack more first-place votes against him.
>> Unfortunately, it's not monotone.
> 
> That's a simple and interesting method. I can see the mechanism is to
> remove control of the *strength* of the Y:Z win from the X voters. Then
> measuring strength as FPs is fairly likely to correctly discard the win
> of the least important candidate.
> 
> I guess that anything else that does something similar would have a
> similar advantage.

FPC has some problems, though, as Jameson Quinn pointed out. It is 
possible to reduce the compromise incentive by doing something like 
Schwartz//FPC (as you'd have to know who would be in the cycle), but 
then it's no longer summable. Note that Schwartz,FPC doesn't reduce the 
compromise incentive as much.

So let's consider what properties a base method must satisfy. Say we 
have X, Y, and Z. Y is the CW, and X voters want to bury Y so that 
X>Y>Z>X in that order of strength. If they accomplish this, Y will be 
beaten by X and Z, so the property should be:

Voters who vote Y below top must not be able to increase the scores of X 
and Z by burying Y.

Or, a weaker criterion:

A ballot that ranks Y last must not decrease the points given to the 
candidates still ahead of Y if Y is raised. (This is just considering 
from the reverse situation, "after" the burial, wrt before the burial.)

The only two methods I can see that satisfy the former are FPP and 
Approval with implicit cutoff. But if you have Approval, you can just as 
easily use C//A and not have to deal with nonmonotonicity.

The weaker criterion seems to be some variant of Later-no-harm, but not 
exactly LNHarm. The point of the weaker criterion is that it should be 
obvious to the X voters that turning X>Y>Z into X>Z>Y will elect Z 
before it elects X. But it doesn't quite feel right...

Any ideas as to which methods could be used?

Perhaps burial/compromising incentive in Condorcet ultimately resolves 
to the same sort of Approval chicken. In a method like FPC with three 
candidates, it's no problem voting sincerely when the third candidate is 
weak (and buriers pose no threat under conventional Condorcet methods 
when the same is the case), and by symmetry, it also isn't a problem 
when the "third" candidate is by far the strongest, but when they're 
equal, then strategy can work -- and this is also where Approval runs 
into trouble.

Yet some Condorcet methods resist strategy better than others. In 
particular, certain nonmonotone methods seem to do so well. Maybe this 
involves the risk of the burial going badly - if it's chaotic (not 
monotone), the buriers won't know when it could backfire and when it 
couldn't. Not so sure about that, either.