Dominant mutual third set

The dominant mutual third set is a set of candidates such that every candidate within the set pairwise-beats every candidate outside the set, and more than one-third of the voters prefer the members of the set to every non-member of the set.

It was first defined by James Green-Armytage as a more particular version of the mutual majority set.

Instant-runoff voting always elects a winner from the smallest dominant mutual third set, just like it does from the smallest mutual majority set. Chris Benham later determined that IRV and Smith,IRV also meet dominant mutual third burial resistance: raising a candidate not in the smallest dominant mutual third set cannot make that candidate the IRV winner.