Mutual majority criterion

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The Mutual majority criterion is a criterion for evaluating voting systems. It applies to ranked ballot elections. It can be stated as follows:

If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.

This is often called Majority criterion for solid coalitions or simply Majority criterion.

Systems which pass:

Borda-Elimination, Bucklin, Coombs, IRV, Kemeny-Young, Nanson (original), Pairwise-Elimination, Ranked Pairs, Schulze, Smith//Minmax, Descending Solid Coalitions, Majority Choice Approval

Systems which fail:

Black, Borda, Dodgson, Minmax, Sum of Defeats