Editing Marquis de Condorcet (section)

==Election methods==
{{main|Condorcet method}}

In 1785, Condorcet published one of his most important works, ''Essay on the Application of Analysis to the Probability of Majority Decisions'' ({{lang|fr|Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix}}).<ref>{{cite book| url=http://gallica.bnf.fr/ark:/12148/bpt6k417181
| title=Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix | format=PNG | language=fr | access-date=2008-03-10 | author=Marquis de Condorcet | year=1785 }}</ref> It described several now-famous results, including [[Condorcet's jury theorem]], which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and [[Condorcet's paradox]], which shows that majority preferences can become [[intransitivity|intransitive]] with three or more options&nbsp;– it is possible for a certain electorate to express [[Rock paper scissors|a preference for A over B, a preference for B over C, and a preference for C over A]], all from the same set of ballots.<ref>{{cite book|author=Douglas J. Amy|title=Behind the Ballot Box: A Citizen's Guide to Voting Systems|url=https://books.google.com/books?id=-G46rVRXkY0C&pg=PA188|year=2000|publisher=Greenwood Publishing Group|page=188|isbn=978-0275965860}}</ref>

The paper also outlines a generic [[Condorcet method]], designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by [[Jean-Charles de Borda]] (based on summed [[Non-parametric statistics|rankings of alternatives]]). Condorcet was one of the first to systematically apply mathematics in the [[social sciences]].{{citation needed|date=April 2018}}

He also considered the [[instant-runoff voting]] elimination method, as early as 1788, though only to condemn it, for its ability to eliminate a candidate preferred by a majority of voters.<ref name=":03">{{Cite journal |last=Nanson |first=E. J. |date=1882 |title=Methods of election: Ware's Method |url=https://archive.org/details/transactionsproc1719roya/page/206 |journal=Transactions and Proceedings of the Royal Society of Victoria |volume=19 |pages=206 |quote=The method was, however, mentioned by Condorcet, but only to be condemned.}}</ref><ref>{{Cite book |last=Condorcet |first=Jean-Antoine-Nicolas de Caritat |url=https://books.google.com/books?id=d0cwAAAAYAAJ&q=Oeuvres+de+Condorcet%2C+Volume+13&pg=PA243 |title=On the Constitution and the Functions of Provincial Assemblies |date=1788 |work=Complete Works of Condorcet |volume=13 |publication-date=1804 |pages=243 |language=fr |quote=En effet, lorsqu'il y a plus de trois concurrents, le véritable vœu de la pluralité peut être pour un candidat qui n'ait eu aucune des voix dans le premier scrutin.}}</ref>