Greatest possible consensus winner

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The alternative with the greatest number of consents (or tied with one or more alternatives for the greatest number of consents) in a given election is a greatest possible consensus winner. Any election that has total preference orders submitted by all voters guarantees the existence of such a winner. There may be multiple greatest possible consensus winners. Any unanimous consensus winner is necessarily a greatest possible consensus winner.

Voting Systems[edit | edit source]

Any voting system that guarantees the election of a greatest possible consensus winner satisfies the greatest possible consensus criterion. Approval voting guarantees the election of greatest possible consensus winners, when it ask voters "which alternatives do you consent to?" Disapproval voting guarantees the election of greatest possible consensus winners, when it ask voters "which alternatives do you not consent to?"

Voting systems that do not guarantee the election of greatest possible consensus winners include: Condorcet methods, Borda Count, IRV, and plurality voting.

If an assumption is made that a voter maximally supports all candidates they consent to, and maximally opposes all candidates they don't consent to (for voting systems with equal-ranking allowed, this means equally ranking all consented-to candidates first, and equally ranking all other candidates last. For rating systems, this means giving the maximal rating to consented-to candidates, and giving the minimal rating to all other candidates), then the following voting systems guarantee the election of greatest possible consensus winners: Condorcet methods with equal-ranking allowed, and Score Voting.