# MAM

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.

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:

**MAM:**

Note that paragraph 6 concisely defines MAM. The other paragraphs are merely supporting-definitions for paragraph 6.

(Paragraphs 1 through 4 are common to many other voting systems)

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.

[end of MAM definition]

For much more information about MAM, including a differently-worded definition, go to the above-linked-to MAM page by Steve Eppley.