Majority loser criterion
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
Either of the Condorcet loser criterion or the mutual majority criterion implies the majority loser criterion. However, the Condorcet criterion does not imply the majority loser criterion (though the Generalized Condorcet criterion does). Neither does the majority criterion imply the majority loser criterion (because the majority is only united in preferring any candidate over the majority loser; they may not necessarily have a single 1st choice candidate that must win).
Methods that comply with this criterion include Schulze, ranked pairs, Kemeny–Young, Nanson, Baldwin, Coombs, Borda, Bucklin, instant-runoff voting, contingent voting, and anti-plurality voting.
Methods that do not comply with this criterion include plurality, MiniMax, Sri Lankan contingent voting, supplementary voting, approval voting, and range voting.
Notes
The majority loser criterion could be generalized into the mutual majority loser criterion: if a majority prefers any candidates other than those in a given set, then the candidates in the set must not win.