Forest Simmons fsimmons at pcc.edu
Sat Oct 1 12:09:16 PDT 2016

Here's an idea for fixing MMPO's lack of  Plurality compliabnce:

Include the opposition of the Implicit Approval Cutoff Candidate, the
virtual candidate on the truncation boundary.


40 A
10 C>A
10 C>B
40 B

In regular MMPO, the max opposition to C is 40.  But when the number of
ballots on which C is truncated is counted among the oppositions, the max
opposition becomes 80.  Thus Plurality is rescued.

How about the Chicken problem?


49 C
3 A  (sincere A>B)
24 A>B
24 B (sincere B>A)

Regular MMPO gives A the win contrary to Plurality.
Taking the truncation opposition into account we have max oppositions for
A, B, and C, respectively, as  73, 52, and 51.  Candidate C wins, punishing
B's defection.  This only required three of the A supporters to truncate B.

Unfortunately, even this new version of MMPO fails Condorcet Loser and
Clone Winner.
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