[EM] MMPO
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.
Example:
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?
Consider
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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