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#REDIRECT [[Maximize Affirmed Majorities]] |
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MAM stands for [[Maximize Affirmed Majorities]]. That link leads to Steve Eppley's page about MAM, which includes a definition, properties, and additional information, and comparison to other somewhat similar methods. |
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This page gives a slightly differently-worded definition of MAM, probably a little briefer. It's a time-independent definition, which contributes to its brevity and simplicity: |
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---- |
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'''MAM:''' |
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Note that paragraph 6 concisely defines MAM. The other paragraphs are merely supporting-definitions for paragraph 6. |
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(Paragraphs 1 through 4 are common to many other voting systems) |
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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. |
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2. If X beats Y, then there is said to be a "defeat" of Y, by X. "XY" refers to that defeat. |
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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. |
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...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. |
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If neither XY nor AB is stronger than the other, then they're "equal". |
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4. A "cycle" is a sequence of defeats in which each defeat's defeated candidate is the defeating candidate in the next defeat, |
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and in which the sequence's initial defeating candidate is the defeated candidate in the sequence's last defeat. |
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5. A defeat "contradicts" a set of other defeats iff it is in a cycle consisting only of it and them. |
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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". |
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7. How to determine two defeats' dominance-order: |
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...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. |
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...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. |
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...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. |
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...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. |
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8. A candidate wins if s/he has no not-discarded defeats. |
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[end of MAM definition] |
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For much more information about MAM, including a differently-worded definition, go to the above-linked-to MAM page by Steve Eppley. |
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[[Category:Condorcet methods]] |
Latest revision as of 03:40, 26 December 2019
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