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Maximize Affirmed Majorities: Difference between revisions
Linking to Stephen Eppley, Nicolaus Tideman, and Mike Ossipoff
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(Linking to Stephen Eppley, Nicolaus Tideman, and Mike Ossipoff) |
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'''Maximize Affirmed Majorities''' (MAM) is a [[voting method]] developed by [[Stephen Eppley]] that selects a single winner using votes that express each voter's order of preference. MAM also constructs the complete order of finish, and is defined in terms of constructing the "best" order of finish.
A simple summary of it is that it looks at all [[Pairwise matchup|pairwise matchups]], orders them from strongest (largest) to weakest (smallest), and starting from the first defeat, fixes the winner of the pairwise matchup higher in the [[Order of finish|order of finish]] than the loser, and repeats this for all successive defeats (if doing this for a particular defeat would contradict a previous fixed ranking, then that defeat is ignored). The winner is the candidate or candidate(s) who are in 1st place in the constructed order of finish.
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Like many Condorcet methods, MAM always elects a candidate in the Smith set (a.k.a. top cycle), which is the smallest non-empty subset of the candidates such that, for each candidate x in the subset and each candidate y outside the subset, a majority rank x over y. (When there is a Condorcet winner, it alone is in the Smith set.) Requiring that the winner be in the Smith set generalizes the Condorcet criterion to the case where there is not necessarily a Condorcet winner and has a similar justification. With MAM, all candidates in the Smith set finish over all candidates outside the Smith set.
MAM satisfies numerous desirable criteria, including [[Nicolaus Tideman]]'s independence from clone alternatives, Peyton Young's local independence from irrelevant alternatives, [[Mike Ossipoff]]'s strong defensive strategy criterion, weak defensive strategy criterion and truncation resistance, and Eppley's immunity from majority complaints. (Only MAM and extremely similar variations satisfy immunity from majority complaints.)
MAM is highly deterministic, satisfying the resolvability and reasonable determinism criteria. To a casual observer, MAM may appear less deterministic than it is. When sorting the majorities into the largest-to-smallest order of precedence, the order in which same-size majorities are sorted would depend on chance. That often won't affect the order of finish. Even when it does affect the order of finish, it often doesn't affect which alternative finishes on top, which is the common standard for evaluating determinism.
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