Editing Condorcet paradox (section)

== History ==
Condorcet's paradox was first discovered by [[Catalonia|Catalan]] [[philosopher]] and [[Theology|theologian]] [[Ramon Llull]] in the 13th century, during his investigations into [[church governance]], but his work was lost until the 21st century. The mathematician and political philosopher [[Marquis de Condorcet]] rediscovered the paradox in the late 18th century.<ref>{{cite book |author=Marquis de Condorcet |author-link=Marquis de Condorcet |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 |year=1785 |language=fr |format=PNG |access-date=2008-03-10}}</ref><ref>{{Cite book |last1=Condorcet |first1=Jean-Antoine-Nicolas de Caritat |title=The political theory of Condorcet |last2=Sommerlad |first2=Fiona |last3=McLean |first3=Iain |date=1989-01-01 |publisher=University of Oxford, Faculty of Social Studies |location=Oxford |pages=69–80, 152–166 |oclc=20408445 |quote=Clearly, if anyone's vote was self-contradictory (having cyclic preferences), it would have to be discounted, and we should therefore establish a form of voting which makes such absurdities impossible}}</ref><ref>{{Cite journal |last=Gehrlein |first=William V. |year=2002 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |journal=Theory and Decision |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=0040-5833 |s2cid=118143928 |quote=Here, Condorcet notes that we have a 'contradictory system' that represents what has come to be known as Condorcet's Paradox.}}</ref>

Condorcet's discovery means he arguably identified the key result of [[Arrow's impossibility theorem]], albeit under stronger conditions than required by Arrow: Condorcet cycles create situations where any ranked voting system [[May's theorem|that respects majorities]] must have a [[spoiler effect]].