Arrow's impossibility theorem
Result that no ranked-choice system is spoilerproof / From Wikipedia, the free encyclopedia
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Arrow's impossibility theorem is a key result in social choice showing that no ranked-choice voting rule[note 1] can produce a logically coherent result when there are more than two candidates. Specifically, any such rule violates independence of irrelevant alternatives: the principle that a choice between and should not depend on the quality of a third, unrelated outcome .[1][2]
The result is often cited in discussions of election science and voting theory, where is called a spoiler candidate. As a result, Arrow's theorem can be restated as saying that no ranked voting system can eliminate the spoiler effect.[3][4][5]
The practical consequences of the theorem are debatable, with Arrow himself noting "Most [ranked] systems are not going to work badly all of the time. All I proved is that all can work badly at times."[4][6] The susceptibility of different systems to spoiler paradoxes varies greatly. Plurality, Borda, and instant-runoff suffer spoiler effects more often than other methods,[7] even in situations where spoiler effects are not forced.[8][9] By contrast, majority-choice methods uniquely minimize the effect of spoilers on elections,[10] limiting them to rare[11][12] situations known as voting paradoxes.[8]
While originally overlooked, a large class of systems called rated methods are not affected by Arrow's theorem or IIA failures.[13][3][5] Arrow initially asserted the information provided by these systems was meaningless, and therefore could not prevent his paradox.[14] However, he would later recognize this as a mistake,[4][15] describing score voting as "probably the best" way to avoid his theorem.[16][17][18]