Arrow's impossibility theorem
Proof that no ranked-choice system is spoilerproof / From Wikipedia, the free encyclopedia
Arrow's impossibility theorem is a key result in social choice showing that no rank-based procedure for collective decision-making can behave rationally or coherently. 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 option
.[1][2]
The result is most often cited in election science and voting theory, where is called a spoiler candidate. In this context, Arrow's theorem can be restated as showing that no ranked-choice voting rule[note 1] can eliminate the spoiler effect.[3][4][5]
Some methods are more susceptible to spoilers than others. Plurality and instant-runoff in particular are highly sensitive to spoilers,[6][7] often manufacturing them even in situations where they are not forced.[8][9] By contrast, Condorcet methods minimize the possibility of spoilers.[10] In other words, a ranked voting system can always be made limiting them to rare[11][12] situations called Condorcet paradoxes.[8] As a result, the practical consequences of the theorem are debatable, with Arrow 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][13]
While originally overlooked by Arrow, rated methods are not affected by Arrow's theorem or IIA failures.[14][3][5] Arrow initially asserted the information provided by these systems was meaningless,[15] and therefore could not be used to prevent paradoxes. However, he and other authors[16] would later recognize this to have been a mistake,[17] with Arrow admitting systems based on cardinal utility (such as score and approval voting) are not subject to his theorem.[18][19][20]