Resistant set

The resistant set or inner burial set is a set defined for strict rank-order preferences, where electing from the set confers burial resistance. It was devised by Kristofer Munsterhjelm in 2023.

Definition

A sub-election of an election is the resulting election after some candidates have been eliminated and preferences transferred.

A candidate X disqualifies another candidate Y if: in every sub-election where X and Y are both present, X has more than 1/k of the first preferences, where k is the number of non-eliminated candidates in that sub-election.

The resistant set consists of every candidate who is not disqualified by someone else.

Properties

The set itself is monotone, as raising candidate X can't decrease his first preference count in any sub-election, nor can it raise someone else above the 1/k threshold who wasn't already above it.

Methods that elect from this set automatically pass dominant mutual third candidate resistance, and in the three-candidate case, also the full dominant mutual third criterion.

However, methods of the type Resistant//M fail monotonicity if M passes the majority criterion. Although Yee diagrams and numerical simulations suggest that there exist methods of the form Resistant,M that are monotone, this has not been proven.

Generalizations

The resistant set may be generalized to elections that allow equal-rank and truncation, but in this case, two properties must be true:

• The total number of first preferences in a sub-election does not include voters who rank every non-eliminated candidate equal.
• No voter has more then unit voting weight in total when counting first preferences. In particular A=B=C>D can't be counted as giving one vote to all of A, B, and C.

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