Editing Gibbard–Satterthwaite theorem (section)

==History==
The strategic aspect of voting is already noticed in 1876 by Charles Dodgson, also known as [[Lewis Carroll]], a pioneer in social choice theory. His quote (about a particular voting system) was made famous by [[Duncan Black]]:<ref>{{Cite book|title=The theory of committees and elections|last=Black|first=Duncan|publisher=University Press|year=1958|location=Cambridge}}</ref><blockquote>This principle of voting makes an election more of a game of skill than a real test of the wishes of the electors.</blockquote>During the 1950s, [[Robin Farquharson]] published influential articles on voting theory.<ref>{{cite journal|last=Farquharson|first=Robin|date=February 1956|title=Straightforwardness in voting procedures|journal=Oxford Economic Papers |series=New Series|volume=8|issue=1|pages=80–89|jstor=2662065|author-link=Robin Farquharson|doi=10.1093/oxfordjournals.oep.a042255|doi-access=free}}</ref> In an article with [[Michael Dummett]],<ref>{{cite journal|last2=Farquharson|first2=Robin|date=January 1961|title=Stability in voting|journal=Econometrica|volume=29|issue=1|pages=33–43|doi=10.2307/1907685|jstor=1907685|first1=Michael|last1=Dummett}}</ref> he conjectures that deterministic voting rules with at least three outcomes are never straightforward [[tactical voting]].<ref>{{cite journal|last=Dummett|first=Michael|year=2005|title=The work and life of Robin Farquharson|journal=Social Choice and Welfare|volume=25|issue=2|pages=475–483|doi=10.1007/s00355-005-0014-x|jstor=41106711|s2cid=27639067}}</ref> This conjecture was later proven independently by [[Allan Gibbard]] and [[Mark Satterthwaite]]. In a 1973 article, Gibbard exploits [[Arrow's impossibility theorem]] from 1951 to prove the result we now know as [[Gibbard's theorem]].<ref name="gibbard"/> Independently, Satterthwaite proved the same result in his PhD dissertation in 1973, then published it in a 1975 article.<ref name="satterthwaite"/> This proof is also based on Arrow's impossibility theorem, but does not involve the more general version given by Gibbard's theorem.