Immune set

Immune set: The set of candidates such that any pairwise defeat against a candidate within the set is countered by a string of stronger pairwise defeats leading back to the defeating candidate.

There is an immune set definition for various possible defeat strength definition, e.g. the WV-defined immune set, the margins-defined immune set, the CWP-defined immune set. It is based on the concept of beatpath strength.

If there is a Condorcet winner, he or she is the only member of the immune set. In a three candidate cycle with unequal defeat strengths, the immune set has one member, i.e. the candidate with the weakest defeat against him or her. When defeats in a cycle have equal strength, or when the cycle is between more than three candidates, the immune set can have multiple members.

The immune set was proposed by Jobst Heitzig.

The immune set is a subset of the Smith set, because the candidates in the Smith set have no defeats against them. When there is a 3-candidate Smith set with no pairwise ties between them, the Smith//Minimax winner is the only candidate in the immune set. Because of this, the immune set has a strong connection to defeat-dropping Condorcet methods.