Greatest possible consensus winner

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
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.