[EM] Defection, nomination disincentive, MMPO

[Kevin Venzke]

Hello,

Consider these sincere preferences:
49 A>B=C
2? B>C>A
2? C>B>A
100 total

The supporters of B and C, 51% of the voters, agree that A is
the worst candidate. But ensuring that the B and C voters can
cooperate may be difficult, since B supporters want B to win
if possible, and the same is true with the C supporters. 

In IRV, B supporters might try to communicate to the C voters
that they won't give a second preference vote to C. This could
happen particularly if B has major party support, and C is just
a like-minded independent. The result of this voting behavior
might be:
49 A
24 B
27 C>B

If, as above, C receives more first preferences than B, B will
be eliminated first and A will win. Thus the result of the B
supporters' stance may be that C decides it is better not to
enter the race at all.

Most WV methods fix this situation by electing B, which seems 
defensible since B receives the most votes of at least some
rank. It seems unreasonable to elect A, since a majority vote
that B is preferred to A.

A problem is that perhaps the B voters are just defecting, in
attempt to steal the election from C. With these ballots:
49 A
24 B>C
27 C>B

WV methods (as well as IRV) elect C. Thus the addition of the
second preference for C, by the B voters, causes B to lose
the election. This is a failure of Later-no-Harm, and perhaps
being aware of this failure, the B voters defect. C voters
could defect, also, concerned about the same problem.  If enough
B and C voters do this, then A will win. And perhaps in order
to avoid this possibility entirely, one of B or C will decide
in advance not to enter the race at all.

I had thought that IRV's approach (elect A and C respectively
in the above scenarios) and WV's approach (elect B and C) were
the only approaches possible, but I've noticed another one.

In "MinMax (Pairwise Opposition)" or "MMPO," a pairwise matrix
is formed as in a Condorcet method, but the winners of pairwise
contests are not determined. For each candidate, find how many 
ballots favored each other candidate over him, and record the 
largest number. Elect the candidate for whom this number is smallest.

This method has flaws: It fails Condorcet, Majority, Plurality,
and Clone Independence. But it does satisfy Later-no-Harm. Here
is how it handles both of the above scenarios:

49 A, 24 B, 27 C>B or
49 A, 24 B>C, 27 C>B:
A: score is 51 (number of B>A voters)
B: score is 49 (number of A>B voters)
C: score is 49 (number of A>C voters)

In other words, a B-C tie, regardless of how many B or C voters
defect from the other, so long as over 49 voters rank the same
candidate above A. If at least 25 A voters pick a side between
B and C, then that would break the tie, also.

If a tie still remains, I suggest breaking it with Random Ballot
or perhaps FPP, two methods which still satisfy Later-no-Harm.

I don't think this would eliminate defections and nomination
disincentive, but I think it would go a long way.

Any thoughts?

Kevin Venzke



	

	
		
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