Arrow's impossibility theorem in the context of "Median voter"

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⭐ Core Definition: Arrow's impossibility theorem

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option, C.

The result is often cited in discussions of voting rules, where it shows no ranked voting rule can eliminate the spoiler effect. This result was first shown by the Marquis de Condorcet, whose voting paradox showed the impossibility of logically-consistent majority rule; Arrow's theorem generalizes Condorcet's findings to include non-majoritarian rules like collective leadership or consensus decision-making.

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👉 Arrow's impossibility theorem in the context of Median voter

In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a political spectrum, any Condorcet consistent voting method will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem does not apply, and rational choice is possible for societies. The theorem was first derived by Duncan Black in 1948, and independently by Kenneth Arrow.

Similar median voter theorems exist for rules like score voting and approval voting when voters are either strategic and informed or if voters' ratings of candidates fall linearly with ideological distance.

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Arrow's impossibility theorem in the context of Spoiler effect

In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof and satisfy independence of irrelevant alternatives.

The frequency and severity of spoiler effects depends substantially on the voting method. First-past-the-post voting without winnowing or primary elections is sensitive to spoilers. And so, to a degree, are Instant-runoff or ranked-choice voting (RCV) and the two-round system (TRS). Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare situations called cyclic ties. Rated voting systems are not subject to Arrow's theorem, allowing them to be spoilerproof so long as voters' ratings are consistent across elections.

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Arrow's impossibility theorem in the context of Kenneth Arrow

Kenneth Joseph Arrow (August 23, 1921 – February 21, 2017) was an American economist, mathematician and political theorist. He received the John Bates Clark Medal in 1957, and the Nobel Memorial Prize in Economic Sciences in 1972, along with John Hicks.

In economics, Arrow was a major figure in postwar neoclassical economic theory. Four of his students (Roger Myerson, Eric Maskin, John Harsanyi, and Michael Spence) went on to become Nobel laureates themselves. His contributions to social choice theory, notably his "impossibility theorem", and his work on general equilibrium analysis are significant. His work in many other areas of economics, including endogenous growth theory and the economics of information, was also foundational.

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LINKED FROM (PARENTS)
← Median voter ← Spoiler effect ← Vote splitting ← Kenneth Arrow
LINKS TO (CHILDREN)
Social choice theory → Ordinal utility → Rational choice → Kenneth Arrow → Independence of irrelevant alternatives → Electoral system → Ranked voting → Spoiler effect → Marquis de Condorcet → Voting paradox → Majority rule → Generalization → Collective leadership → Consensus decision-making →