Immune set

Immune set: The set of candidates such that any defeat against a candidate within the set is countered by a string of stronger (or equally strong) 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.

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.