Voice of reason

The voice of reason voting method is a single-winner method proposed by Burt Monroe.

Definition
Monroe defines the system as follows:

"For any set of alternatives, we can look at each pair and determine which of the pair is preferred by a majority. The voice of reason finds the single voter who agrees with the most majorities and selects that voter's first preference. In more intuitive language, the system finds the single most 'moderate' voter and selects his or her first choice."

More formally, let the scoring function $$f(V, A, B)$$ be $$1$$ if A beats B pairwise and voter V also ranks A ahead of B, $$0$$ otherwise; and let $$f(V) = \sum_{A,B} f(V, A, B)$$. The method then ranks the candidates in the same way that the voter $$V^*$$ with the greatest value of $$f$$ does. In particular, the candidate ranked first by $$V^*$$ wins.

Criterion compliances
It is monotone and always elects a candidate with at least one first preference. It thus fails the Condorcet criterion and passes the Majority criterion. It also passes the mutual majority criterion.

The voice of reason fails clone independence. Suppose that A wins due to some ballot that ranks A>B>C>D being selected, and on some other ballot, B>A>C>D. Now clone C into clones C1...Cn so that society's pairwise preferences are C1>C2>...>Cn, and let the A-first ballots rank the C clones in some other order whereas the B-first ballots rank the C clones in this order. This will increase the B-first ballots' score relative to the A-ballots and may make B win.

Burt Monroe suggested that methods that fail his Nonelection of Irrelevant Alternatives criterion are quickly abandoned in practice due to strategic voting making them elect candidates who are universally considered to be worst. Like the First Past the Post electoral system, runoff voting, and IRV, the voice of reason method passes this criterion.

Despite passing Monroe's NIA criterion, the voice of reason fails dominant mutual third burial resistance, demonstrating that NIA doesn't require DMTBR.