Editing Arrow's impossibility theorem (section)

== Common misconceptions ==
Arrow's theorem is not related to [[strategic voting]], which does not appear in his framework,<ref name="Arrow 1963234"/><ref name="plato.stanford.edu"/> though the theorem does have important implications for strategic voting (being used as a lemma to prove [[Gibbard's theorem]]<ref name="Gibbard1973"/>). The Arrovian framework of [[Social welfare function|social welfare]] assumes all voter preferences are known and the only issue is in aggregating them.<ref name="plato.stanford.edu" />

[[Monotonicity criterion|Monotonicity]] (called [[Positive response|positive association]] by Arrow) is not a condition of Arrow's theorem.<ref name="Arrow 1963234" /> This misconception is caused by a mistake by Arrow himself, who included the axiom in his original statement of the theorem but did not use it.<ref name="Arrow1950" /> Dropping the assumption does not allow for constructing a social welfare function that meets his other conditions.<ref name="Arrow 1963234" />

Contrary to a common misconception, Arrow's theorem deals with the limited class of [[Ranked voting|ranked-choice voting systems]], rather than voting systems as a whole.<ref name="plato.stanford.edu" /><ref>{{cite web |last1=Hamlin |first1=Aaron |date=March 2017 |title=Remembering Kenneth Arrow and His Impossibility Theorem |work=The Center for Election Science |url=https://electionscience.org/commentary-analysis/voting-theory-remembering-kenneth-arrow-and-his-impossibility-theorem/ |access-date=5 May 2024 |publisher=Center for Election Science}}</ref>