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Maximize Affirmed Majorities: Difference between revisions
reasonably quick merge of MAM into this page
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In some situations, a very large majority may be required to enact certain changes. For instance, a 3/4 supermajority might be needed to amend a group's charter. Continuing the status quo is a highly privileged alternative. What voting method should be used if more than one change is proposed, and the changes conflict so they can't all pass? They can be voted on using MAM. (Continuing the status quo would be an alternative too.) If the status quo tops the order of finish, or if the alternative that tops the order of finish isn't ranked over the status quo by a sufficiently large supermajority, then the status quo wins. Otherwise the alternative atop the order of finish wins (and becomes the new status quo).
== Mike Ossipoff's restatement of MAM ==
[[User:MichaelOssipoff]] proposed the following definition of MAM, which is copied here from the for [[MAM]] page
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1. X beats Y iff the number of ballots ranking X over Y is greater than the number of ballots ranking Y over X.
2. If X beats Y, then there is said to be a "defeat" of Y, by X. "XY" refers to that defeat.
3. XY is "stronger" than AB iff the number of ballots ranking X over Y is greater than the number of ballots ranking Y over X.
...but if those numbers are equal, then XY is stronger than AB iff the number of ballots ranking B over A is greater than the number of ballots ranking Y over X.
If neither XY nor AB is stronger than the other, then they're "equal".
4. A "cycle" is a sequence of defeats in which each defeat's defeated candidate is the defeating candidate in the next defeat,
and in which the sequence's initial defeating candidate is the defeated candidate in the sequence's last defeat.
5. A defeat "contradicts" a set of other defeats iff it is in a cycle consisting only of it and them.
6. A defeat is a "discarded defeat" iff it contradicts a set of not-discarded defeats each of which is either stronger than it, or equal to it and above it in the "dominance-order".
7. How to determine two defeats' dominance-order:
...a) Randomly choose one of the election's ballots. It will be referred to as the "comparison-ballot", and used as such for entire count, for all defeat-dominance-order comparisons.
...b) If XY and AB are equal (neither stronger than the other, as defined above), then XY is above AB in the dominance order iff B is ranked higher than Y on the comparison ballot.
...c) ...but if the comparison-ballot ranks Y and B equal (at the same rank-position), then XY is above AB in the dominance-order iff X is ranked higher than A on the comparison-ballot.
...d) If XY and AB are equal, and if, by b) and c), neither XY nor AB is above the other in the dominance-order, then randomly choose another ballot as the comparison-ballot, for the purpose of comparing XY and AB with regard to dominance-order.
8. A candidate wins if s/he has no not-discarded defeats.
== External Resources ==
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