Minimal Defense criterion

From electowiki

The Minimal Defense criterion for voting systems is similar to and was inspired by the Strong Defensive Strategy criterion. It is stronger than the SDSC and implies it.[1]

Statement of Criterion

Stephen Eppley gives this official definition:

If more than half of the voters prefer alternative y over alternative x, then that majority must have some way of voting that ensures x will not be elected and does not require any of them to rank y equal to or over any alternatives preferred over y.

This definition is most similar to that of SDSC. Another definition suggested by Eppley makes reference only to the cast votes:

If more than half of the voters rank Y above X, and X above no other candidate, then X must not be elected.

It's also required that the method permits voters to submit complete or incomplete rankings. In particular, truncation must be an option: It's not adequate for the method to require that the voters rank X strictly below every other candidate.

Complying Methods

Methods satisfying Minimal Defense include Steve Eppley's own Maximize Affirmed Majorities method, Schulze using winning votes as the measure of defeat strength, Jobst Heitzig's River method, Bucklin voting, methods electing from the CDTT set, MDDA, MAMPO, and Condorcet//Approval.


In a method that satisfies Minimal Defense, when a majority of the voters prefer candidate A to candidate B, all that these voters need to do to avoid the election of B is to not give B a ranking over another candidate.

In particular, even if all of the voters preferring A to B each prefer many other different candidates to A, Minimal Defense guarantees that these voters don't need to insincerely rank A above or even equal to these other candidates to ensure that B won't be elected.


  1. Venzke, K. (2005-03-05). "A method satisfying Minimal Defense and much Later-no-harm". Election-methods mailing list archives.

External links