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Arrow's impossibility theorem is a key result in social choice showing that no order or rank-based social welfare function can produce a rational measure of society's well-being when there are more than two options. Specifically, any such rule violates independence of irrelevant alternatives: the principle that a choice between and should not depend on a third, unrelated option .[1][2] Such a social welfare function can be any way for a group to make decisions, such as a market or a voting system.[3]
However, the result is perhaps most famously 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.[4][5][6]
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."[5][7] Plurality, Borda, and instant-runoff are all highly sensitive to spoilers,[8][9] often manufacturing them even in situations where they are not forced.[10][11] By contrast, Condorcet methods uniquely minimize the effect of spoilers on elections,[12] limiting them to rare[13][14] situations known as Condorcet paradoxes.[10]
While originally overlooked by Arrow, rated methods are not affected by Arrow's theorem or IIA failures.[15][4][6] Arrow initially asserted the information provided by these systems was meaningless,[16] and therefore could not be used to prevent paradoxes. However, he and other authors[17] would later recognize this to have been a mistake,[18] with Arrow admitting systems based on cardinal utility (such as score and approval voting) are not subject to his theorem.[19][20][21]
:3
was invoked but never defined (see the help page).Arrow 19632
was invoked but never defined (see the help page).plato.stanford.edu
was invoked but never defined (see the help page).In the present stage of the discussion on the problem of social choice, it should be common knowledge that the General Impossibility Theorem holds because only the ordinal preferences is or can be taken into account. If the intensity of preference or cardinal utility can be known or is reflected in social choice, the paradox of social choice can be solved.
The abandonment of Condition 3 makes it possible to formulate a procedure for arriving at a social choice. Such a procedure is described below
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does not do away with the spoiler problem entirely, although it ... makes it less likely
:2
was invoked but never defined (see the help page).IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. [...] Approval voting thus appears to solve the problem of vote splitting simply and elegantly. [...] Range voting solves the problems of spoilers and vote splitting
:5
was invoked but never defined (see the help page).It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates — avoiding the celebrated impossibility theorem by making use of information which is unavailable in Arrow's original framework.
Dr. Arrow: Well, I’m a little inclined to think that score systems where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best.
Dr. Arrow: Well, I’m a little inclined to think that score systems where you categorize in maybe three or four classes (in spite of what I said about manipulation) is probably the best.[...] And some of these studies have been made. In France, [Michel] Balinski has done some studies of this kind which seem to give some support to these scoring methods.
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