Raynaud

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Raynaud or Pairwise-Elimination is a Condorcet method in which the loser of the strongest pairwise defeat is repeatedly eliminated until only one candidate remains. Defeat strength is usually measured as either the absolute number of votes cast for the winning side (winning votes), or the number of votes for the winning side minus those for the losing side (margins).

Raynaud fails the Monotonicity criterion. Even when winning votes are used as the measure of defeat strength, Raynaud fails the Plurality criterion and the Strong Defensive Strategy criterion.

A variant called Raynaud(Gross Loser) does satisfy the Plurality criterion. It successively eliminates the candidate with the fewest votes for him in any pairwise contest. In this way, it is not possible to eliminate candidate A before candidate B when A has more first preferences than B has any preferences, since this situation means that the minimum number of votes for A in any contest is greater than the maximum number of votes for B in any contest. This variant was devised by Chris Benham.

Raynaud does satisfy the Smith criterion.