Editing Arrow's impossibility theorem (section)

==== Independence ====
A commonly-considered axiom of [[Decision theory|rational choice]] is ''[[independence of irrelevant alternatives]]'' (IIA), which says that when deciding between {{math|''A''}} and {{math|''B''}}, one's opinion about a third option {{math|''C''}} should not affect their decision.<ref name="Arrow1950"/>
* '''''[[Independence of irrelevant alternatives]] (IIA)''''' – the social preference between candidate {{math|''A''}} and candidate {{math|''B''}} should only depend on the individual preferences between {{math|''A''}} and {{math|''B''}}.
** In other words, the social preference should not change from <math>A \succ B</math> to <math>B \succ A</math> if voters change their preference about whether <math>A \succ C</math>.<ref name="Arrow 1963234"/>
** This is equivalent to the claim about independence of [[Spoiler effect|spoiler candidates]] when using the [[Social welfare function#Constructing a social ordering|standard construction of a placement function]].<ref name="Quesada2002"/>
IIA is sometimes illustrated with a short joke by philosopher [[Sidney Morgenbesser]]:<ref name="Pearce">{{Cite journal |last=Pearce |first=David |title=Individual and social welfare: a Bayesian perspective |url=https://economia.uc.cl/wp-content/uploads/2022/12/Individual-and-Social-Welfare-A-Bayesian-Perspective-1-2.pdf |journal=Frisch Lecture Delivered to the World Congress of the Econometric Society}}</ref>
: Morgenbesser, ordering dessert, is told by a waitress that he can choose between blueberry or apple pie. He orders apple. Soon the waitress comes back and explains cherry pie is also an option. Morgenbesser replies "In that case, I'll have blueberry."
Arrow's theorem shows that if a society wishes to make decisions while always avoiding such self-contradictions, it cannot use ranked information alone.<ref name="Pearce" />