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🕸Fergus Duniho wrote on Tue, Jul 18, 2006 10:01 PM UTC:
Whether we say Alice Chess is in second or third place is going to make no
difference to how MAM operates, because it does not make any use of
absolute ordinal values. What it compares are individual pairs of
candidates. For each pair of candidates, it notes which one has more
frequently been ranked above the other. From this it creates a list of
majorities. A majority is an ordered pair of candidates, which includes
information on how many voters favored each candidate. If there are no
cycles in the list of majorities, then it establishes the final ranking of
the candidates, and the top ranked candidate is the condorcet winner. When
there are cycles in the list, such as (A, B), (B, C), and (C, A), it
derives a subset of the majorities that are consistent with each other,
and it uses this subset to establish the final ranking. It does this by
sorting them, then it goes down the list affirming each pair that is
consistent with all previously affirmed pairs, and affirming additional
pairs that can be logically derived from sets of previously affirmed
pairs. By this method, it maximizes the number of affirmed majorities,
hence the name of the method. The sorting function compares two majorities
only with each other, and when they are equal to each other in all relevant
ways, it sorts them according to the results of the strict tie-break
ranking, which is previously established by randomly picking ballots until
enough preferences are collected to establish a strict ordering of the
candidates. The order in which the majorities go will make a difference
only when there are cycles in the list. When there are no cycles, all
majorities will be affirmed.

In general, placing Alice Chess below both versions of Mir Chess should no
more hurt Alice Chess's chance than placing it below only one game would.
If both versions of Mir Chess come out ahead of Alice Chess, one will be
thrown out, and everything below it will be pulled up in the rankings.
When there are cycles in the votes, this will have no effect on the
ordering of most of the majorities involving Alice Chess. The main effect
it will have will be on the ordering of the majority involving both Alice
Chess and Mir Chess, and, if yours is the deciding vote, it will make it a
majority for Mir Chess rather than Alice Chess. This will increase the
chances of affirming the majority of Mir Chess over Alice Chess.

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