[EM] Defensive strategy for Condorcet methods KM

[Kevin Venzke]

Hi Kristofer,

--- En date de : Mer 15.6.11, Kristofer Munsterhjelm <km_elmet at lavabit.com> a écrit :
> > 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.)

I am not sure I am able to follow this. In the first paragraph, if Y
is the CW, you can't have an X>Y>Z>X cycle created by X voters. I guess
you surely mean X>Z>Y>X. And then the rest of your description is
assuming we're using the penalty point idea. I will try to think about
this later.

> 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?

This may have nothing to do with what you propose, but if we talk about
anti-burial Condorcet methods I think we should not forget methods like
TACC, Condorcet//IRV, and also Condorcet//King of the Hill.

I'm short time and my memory isn't quite perfect. But in TACC it seemed
to me that the anti-burial property was that you needed to be able
to predict the approval order both pre- and post-burial, or it wouldn't
work right. I'm going to kick myself if this is wrong, but I think it
was defined (for 3 candidates) as electing the one who defeated the
approval loser. It smells non-monotonic but I don't think it is.

With C//KOTH the B:C contest (where B is sincere CW and C is pawn) is 
not regarded at all (in a cycle). If there is an A:B or A:C full 
majority, it's over. Otherwise, burial by A voters succeeds.

> 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.

I'd be curious if you have anything in mind besides C//IRV and the
penalty point system. It's interesting to consider what commonalities
there may be.

Kevin Venzke