[EM] MMPO, Majority, Condorcet failures

[Kevin Venzke]

I worked up some examples.

I doubted that three-slot MMPO would still permit Majority
failures, so I tried to make one. This is the closest I could
come:

10 A>BC>D
10 B>CA>D
10 C>AB>D
10 DA>B>C
10 DB>C>A
10 DC>A>B

Half the voters prefer {A,B,C} to D, and MMPO shows a four-way
tie among all candidates.

To create a failure, we need one more voter to prefer ABC to D,
but we need D's MMPO score to drop relative to the others'. I
don't think this is possible.


Now for some Condorcet failures:

30 B>C
19 AB
51 AC
CW is C, but MMPO winner is A.

5 B>C
10 C>A
85 AB
CW is A, but MMPO winner is B.

And I was dismayed to find that it isn't enough to disallow
equal ranking:

29 B
19 A>B
9 A>C
43 C

CW is C, but the MMPO winner is A.

This scenario is particularly interesting because A is either
a "weak centrist" candidate, or else someone taking advantage
of the Later-no-help failure. This might be pretty bad. Suppose
the following results are predicted:

49 Bush
24 Gore
27 Martian candidate

All the Martian supporters need to do is vote "Martian>Gore" to
ensure a Martian-Gore tie. The only way this can be countered
is by Bush and/or Gore voters having the strategic sense to vote
"Bush>Gore" or "Gore>Bush" (keeping in mind that MMPO satisfies
Later-no-harm, and so can't make their favorite lose).

Interesting, I think.

Kevin Venzke



	

	
		
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