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'''Negative vote''', also called '''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.
It was originally proposed by George A.W. Boehm in 1976 in an essay<ref>{{Citation|last=Boehm|first=George A. W.|title=One Fervent Vote against Wintergreen|date=1976|volume=|pages=|type=Unpublished mimeograph}}</ref> sent to various social choice theorists, which referenced the plot of the 1931 musical [[W:Of Thee I Sing|''Of Thee I Sing'']], in which a candidate wins the US presidency despite being a bumbling crook,<ref>{{Cite web|url=https://www.negative.vote/about/|title=About|website=Negative Vote|language=en-US|access-date=2020-04-19}}</ref><ref>{{Cite book|last=Poundstone|first=William|url=https://books.google.com/books?id=hbxL3A-pWagC&pg=PA187&lpg=PA187&dq=%22One+Fervent+Vote+against+Wintergreen%22&source=bl&ots=epODeU_CCG&sig=ACfU3U0YgZlvc6ciE-YmlQSzrwsYDtQ9Nw&hl=en&sa=X&ved=2ahUKEwjnrYu5yfXoAhXRlXIEHQppDCgQ6AEwAnoECAsQKQ#v=onepage&q=%22One%20Fervent%20Vote%20against%20Wintergreen%22&f=false|title=Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It)|date=2009-02-17|publisher=Farrar, Straus and Giroux|isbn=978-0-8090-4892-2|language=en|year=|location=|pages=}}</ref>{{Rp|187}} proposing that voters be given the option to vote ''against'' a candidate like Wintergreen rather than ''for'' someone else.
It[[Steven Brams]] was theninitially promotedinterested in negative voting, and analyzed byit for three-candidate elections,<ref>{{Citation|last=Brams|first=Steven J.|title=When is it Advantageous to Cast a Negative Vote?|date=1977|url=http://link.springer.com/10.1007/978-3-642-45494-3_45|work=Mathematical Economics and Game Theory|volume=141|pages=564–572|editor-last=Henn|editor-first=Rudolf|publisher=Springer Berlin Heidelberg|doi=10.1007/978-3-642-45494-3_45|isbn=978-3-540-08063-3|access-date=2020-04-19|editor2-last=Moeschlin|editor2-first=Otto}}</ref> but soon learned of [[Stevenapproval Bramsvoting]] infrom aRobert seriesWeber, ofcompared papersthe two systems,<ref>{{Cite journal|last=Brams|first=Steven|date=1976|title=One Man, n Votes, Module in Applied Mathematics|url=|journal=Mathematical Association of America, Ithaca: Cornell University|volume=|pages=|via=}}</ref><ref>{{Citation|last=Brams|first=Steven J.|title=When is it Advantageous to CastComparison a Negative Vote?Voting|date=19771983|url=http://link.springer.com/10.1007/978-31-6424612-454945430-3_450_3|work=Mathematical EconomicsPolitical and GameRelated TheoryModels|volume=141|pages=564–57232–65|editor-last=Henn|editor-first=Rudolf|publisher=Springer BerlinNew HeidelbergYork|language=en|doi=10.1007/978-31-6424612-454945430-3_450_3|isbn=978-31-5404612-080635432-34|access-date=2020-04-19|editor2-last=Moeschlin|editor2-first=Otto|editor3-last=|editor3-first=}}</ref> and started advocating approval voting instead.<ref>{{Cite book|last=Brams|first=Steven J.|url=https://www.worldcat.org/title/mediawiki/oclc/ocm96045998|title=Approval voting|last2=Fishburn|first2=Peter C.|date=2007|publisher=Springer|isbn=978-0-387-49895-9|edition=2nd ed|location=New York|oclc=ocm96045998}}</ref>{{Rp|xv}}
== Notes ==
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