Resistant set

From electowiki

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.[1]

Definition[edit | edit source]

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[edit | edit source]

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.[2] 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[edit | edit source]

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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References[edit | edit source]

  1. Munsterhjelm, K. (2023-08-16). "The resistant set". Election-methods mailing list archives.
  2. Ejlak, F. (2023-08-16). "Re: The resistant set". Election-methods mailing list archives.