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 logically coherent results with 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]
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.[1][2]
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."[2][3] However, the susceptibility of different systems varies greatly. Plurality, Borda, and instant-runoff suffer spoiler effects more often than other methods,[4] and even in situations where spoiler effects are not necessary,[5][6] as they can elect candidates who would have lost in a straight majority vote. Majority-choice methods uniquely minimize the effect of spoilers on election results, limiting them to rare[7][8] situations known as cyclic ties.[5]
While originally overlooked, a large class of systems called rated methods are not affected by Arrow's theorem or IIA failures.[2][9][10] Arrow himself initially dismissed such systems on philosophical grounds, but later considered this a mistake, describing score voting as "probably the best" way to avoid his paradox.[2][10]