Negative vote

From electowiki

Negative vote, also called bipolar voting[1][2] or balanced plurality voting (BPV)[3] 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[4] 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,[5][6]:187 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,[7] but soon learned of approval voting from Robert Weber, compared the two systems,[8][9] and started advocating for approval voting instead.[2][10]:xv

It is currently advocated by the Negative Vote Association in Taiwan,[11] chiefly by Sam (Tien Shang) Chang, and by NEGATIVE.VOTE in Chicago (though this organization has expanded[3] to adding a negative option to other voting methods as well, such as Balanced Approval, Balanced RCV, etc.)[12]

It is intended to eliminate extremist candidates, empower moderates, encourage positive campaigning,[9]:35 and promote more peaceful politics.[11][5]


Although negative voting is mathematically equivalent to FPTP in two-candidate elections,[7] and equivalent to approval voting in three-candidate elections, the psychological impact of voting against a candidate may nevertheless change voter behavior and turnout.[13]

The common argument Negative vote advocates make is that in a two-faction election, partisans of both sides will "cancel each other out" by putting positive votes on their own side's candidates and negative votes on the other side's candidates, allowing candidates "in the middle" to win with some votes from centrist voters and no opposition from the partisans, who will be more focused on stopping the other side.

Cardinal method advocates tend to argue that negative vote still preserves most of the worst features of FPTP, in that it doesn't allow a voter to support multiple candidates, and can still incentivize Favorite Betrayal.


  1. Ferguson, Daniel; Lowi, Theodore (2001). "Reforming American Electoral Politics: Let's Take "No" for an Answer". Political Science & Politics. 34 (02): 277–280. doi:10.1017/S1049096501000506. ISSN 1049-0965.
  2. a b Brams, Steven J. (2003). ""Bipolar Voting" Not a New Idea". Political Science and Politics. 36 (01). doi:10.1017/S1049096503001586. ISSN 1049-0965.
  3. a b Cohen, Paul (2018-03-23). "Yet Another Balanced Voting Method". OpEdNews. Retrieved 2020-04-20. BPV was the very first example of Balanced Voting (but since then, renamed) to be described in this series of articles.
  4. Boehm, George A. W. (1976), One Fervent Vote against Wintergreen (Unpublished mimeograph)
  5. a b "About". Negative Vote. Retrieved 2020-04-19. curb the influence of extremists on both sides of the political spectrum and empower the middle-minded, moderate majority
  6. Poundstone, William (2009-02-17). Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It). Farrar, Straus and Giroux. ISBN 978-0-8090-4892-2.
  7. a b Brams, Steven J. (1977), Henn, Rudolf; Moeschlin, Otto (eds.), "When is it Advantageous to Cast a Negative Vote?", Mathematical Economics and Game Theory, Springer Berlin Heidelberg, 141, pp. 564–572, doi:10.1007/978-3-642-45494-3_45, ISBN 978-3-540-08063-3, retrieved 2020-04-19
  8. Brams, Steven (1976). "One Man, n Votes, Module in Applied Mathematics". Mathematical Association of America, Ithaca: Cornell University.
  9. a b Brams, Steven J. (1983), "Comparison Voting", Political and Related Models, Springer New York, pp. 32–65, doi:10.1007/978-1-4612-5430-0_3, ISBN 978-1-4612-5432-4, retrieved 2020-04-19
  10. Brams, Steven J.; Fishburn, Peter C. (2007). Approval voting (2nd ed.). New York: Springer. ISBN 978-0-387-49895-9. OCLC 96045998.
  11. a b "About Us". 負數票協會 Negative Vote Association. Retrieved 2020-04-20. will weed out extremist candidates, societies will become more harmonious internally and less likely to go to war against neighbors.
  12. "Home". Negative Vote. Retrieved 2020-04-20.
  13. Baujard, Antoinette; Gavrel, Frédéric; Igersheim, Herrade; Laslier, Jean-François; Lebon, Isabelle (2018). "How voters use grade scales in evaluative voting". European Journal of Political Economy. 55: 6–9. doi:10.1016/j.ejpoleco.2017.09.006. ISSN 0176-2680.