User:BetterVotingAdvocacy/Self-referential Smith-efficient Condorcet method

Self-referential Condorcet methods (SR-Condorcet methods) guarantee the election of a candidate, the SR-Condorcet winner, who would win within the voting method if it was just them and any other candidate, when one exists (related to a Condorcet winner). More broadly, if there are a smallest set of candidates, the SR-Smith set, who would each win if it was just them and any other candidate not in the set, some voting methods always elect someone from this set of candidates (related to the Smith set).

(Note that an underlying assumption is that a voter would cast the same ballot no matter which candidates are added or removed; if voters change their preferences, then most likely no voting method can be an SR-Condorcet method.)

Condorcet methods, Approval voting (which is just a form of Score voting), and Score voting are the most notable such methods. Any voting method that passes the majority criterion in the two-candidate case has to be a Condorcet method to be an SR-Condorcet method. Any voting method that passes the "utility criterion" (i.e. always elects the candidate with the most utility/approval) in the two-candidate case has to be Score voting to be an SR-Condorcet method.

Score voting is SR-Smith-efficient and guarantees there will always be an SR-Smith set of either SR-weak Condorcet winners (candidates who would either tie or win if it was just them and anyone not else) or a single SR-Condorcet winner. The same is not true for Condorcet methods because of Condorcet cycles.