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Because of this example, some authors credit Condorcet with having given an intuitive argument that presents the core of Arrow's theorem. [20] However, Arrow's theorem is substantially more general; it applies to methods of making decisions other than one-man-one-vote elections, such as markets or weighted voting, based on ranked ballots.
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.
Arrow's impossibility theorem states that for three and more candidates, the only unanimous voting rule for which there is always a Condorcet winner is a dictatorship. The usual proof of Arrow's theorem is combinatorial. Kalai [13] gave an alternative proof of this result in the case of three candidates using Fourier analysis.
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
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Area theorem (conformal mapping) (complex analysis) Arithmetic Riemann–Roch theorem (algebraic geometry) Aronszajn–Smith theorem (functional analysis) Arrival theorem (queueing theory) Arrow's impossibility theorem (game theory) Arrow-Lind theorem (welfare economics) Art gallery theorem ; Artin approximation theorem (commutative algebra)
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