[EM] FBC comparison: WV, margins, MMPO, DMC
Kevin Venzke
stepjak at yahoo.fr
Wed Sep 7 13:08:54 PDT 2005
Rob,
--- Rob LeGrand <honky1998 at yahoo.com> a écrit :
> Kevin, could you post an example that gives a favorite-betrayal
> incentive under margins but not winning-votes?
I can do a bit better than this. I can try to explain why we would
expect margins to offer more FB incentive than WV.
The common scenario is that your sincere ranking is A>B>C, and this results
in an A>B>C>A cycle in which B>C is the weakest link, so that C is elected.
It's possible that the only way to get B to win is to reverse the direction
of the A>B win. In this case, WV, margins, and DMC all may offer FB
incentive, since changing your A>B vote to B>A is twice as fast as A=B
at switching around which one of the two wins.
In MMPO, this scenario doesn't exist, because there's no such thing as
"reversing the direction of a win." Essentially every candidate has some
"win" over every other candidate, so all you can do is weaken opposition.
The methods are quite different in the case where it is sufficient to
*weaken* the strength of the A>B win without needing to reverse it.
In WV and MMPO (that is, MinMax(pairwise opposition)), there is never
favorite betrayal in this case, because changing the vote A>B to A=B is
no more effective than changing it to B>A. Every voter making this change
reduces the A>B strength by 1 vote.
But in margins, favorite betrayal always works twice as fast as equal
ranking. Changing A>B to A=B shrinks the margin by 1 vote, while changing
it to B>A shrinks the margin by 2 votes. Sometimes B>A is going to be the
only way to weaken the defeat sufficiently.
In DMC, neither A=B nor B>A is effective. The only ability you have to weaken
the A>B win (assuming you can't reverse it) is to disapprove A!
(My FBC simulation doesn't envision favorite betrayal of that kind, so I
would have to rethink it in order to find statistics for DMC relative to
WV and margins.)
Kevin Venzke
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