Negative vote

Negative vote, also called bipolar voting or balanced plurality voting (BPV) is a modification of FPTP, in which voters can choose to either support a single candidate, or vote against a single candidate. The negative votes are subtracted from positive votes for each candidate, and the candidate with the highest total is the winner.

History and advocacy
It was originally proposed by George A.W. Boehm in 1976 in an essay sent to various social choice theorists, which referenced the plot of the 1931 musical Of Thee I Sing, in which a candidate wins the US presidency despite being a bumbling crook, proposing that voters be given the option to vote against a candidate like Wintergreen rather than for someone else.

Steven Brams was initially interested in Boehm's proposal, and analyzed the system in three-candidate elections, but soon learned of approval voting from Robert Weber, compared the two systems, and started advocating for approval voting instead.

It is currently advocated by the Negative Vote Association in Taiwan, chiefly by Sam (Tien Shang) Chang, and by NEGATIVE.VOTE in Chicago (though this organization has expanded to adding a negative option to other voting methods as well, such as Balanced Approval, Balanced RCV, etc.)

It is intended to eliminate extremist candidates, empower moderates, encourage positive campaigning, and promote more peaceful politics.