Maximize Affirmed Majorities: Difference between revisions

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.

 

Originally MAM was defined as the voting method that finds the order of finish that minimizes the largest "thwarted" majority. (A majority is thwarted if the order of finish does not place their more preferred candidate over their less preferred candidate.) It was originally named "Minimize Thwarted Majorities." The original definition is equivalent (same order of finish) to the quicker procedure with which MAM is more commonly described. (The equivalence is helpful when proving some properties of MAM.) The name was soon changed to MAM to emphasize the positive rather than the negative.

 

Two other voting methods that can be considered close variations of MAM are [[Maximum Majority Voting]] (MMV) and River.

 

One of the main "competing" Condorcet methods is the [[Schulze method]]. Many of the criteria listed above that are satisfied by MAM are also satisfied by Schulze. But not local independence of irrelevant alternatives, nor immunity from majority complaints. (Schulze also fails a weaker immunity criterion, immunity from second place complaints, which requires that the candidate that would win if the winner were deleted must not be ranked over the winner by a majority.) When there are three or fewer candidates, MAM and Schulze always elect the same candidate. When there are four or more candidates, computer simulations independently designed by Norm Petry and Steve Eppley have shown that majorities prefer MAM winners over Schulze winners more often than vice versa.