Majority Approval, Minimum Pairwise Opposition

Majority Approval, Minimum Pairwise Opposition or MAMPO is one method devised by Kevin Venzke for the purpose of showing that the Favorite Betrayal criterion, the Strong Defensive Strategy criterion, and the Strategy-Free criterion are mutually compatible.

Another method with these properties is Majority Defeat Disqualification Approval.

Procedure
The voter submits a ranking of the candidates. The candidates explicitly ranked are considered approved by that voter.

The score for candidate X against candidate Y is equal to the number of voters ranking X above Y. The max score of candidate X is the largest score of any other candidate against X.

If nobody is approved by more than half of the voters, then the candidate approved by the most voters is elected.

Otherwise, the candidate with the lowest max score, who is approved by more than half of the voters, is elected.

Criteria
MAMPO satisfies the Favorite Betrayal criterion, Strategy-Free criterion, the Strong Defensive Strategy criterion (and Minimal Defense criterion), monotonicity, and the Plurality criterion.

It fails Clone-Winner, the Generalized Strategy-Free criterion, the Condorcet criterion, the Smith criterion, Participation, the Majority criterion for solid coalitions, and Later-no-harm.