Kenneth Arrow

Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. He is considered one of the founders of modern (post World War II) neo-classical economics.

General Possibility Theorem

Arrow's impossibility theorem was set out in his Ph.D. thesis, Social choice and individual values.

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In its final form it states the following: given the conditions of Pareto Optimality (P), Unbounded social choice (S), Independence of choices (I) and non-Dictatorship (D), it is impossible to formulate a social choice function which satisfies all of them. This has tremendous implications for welfare economics and theories of justice. It was extended by Amartya Sen to the Liberal Paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto Optimality, nor to avoid the problem of social choice of neutral but unequal results.

Related Topics:
Pareto Optimality - Welfare economics - Justice - Amartya Sen - Liberal Paradox

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An example of this would be to have the following choices to divide a cake between three people. Let us call them A, B and C.

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Choice 1: A gets nothing, B and C get half each.

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Choice 2: B gets nothing, A and C get half each.

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Choice 3: C gets nothing, A and B get half each.

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Choice 4: divide the cake equally.

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Thus choice 4 would be third from the bottom in everyone's list, and would, in any direct choice lose 2 to 1 against an unequal distribution. Since all of these choices are Pareto optimal - no one's welfare can be improved without reducing the welfare of others - choice 4 would not be chosen, since there would always be other preferred choices.

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