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Arrow's theorem assumes as background that any non-degenerate social choice rule will satisfy: [15]. Unrestricted domain — the social choice function is a total function over the domain of all possible orderings of outcomes, not just a partial function.
Unrestricted domain is one of the conditions for Arrow's impossibility theorem. Under that theorem, it is impossible to have a social choice function that satisfies unrestricted domain, Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship. However, the conditions of the theorem can be satisfied if unrestricted domain ...
The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible ...
Arrow's impossibility theorem is a key result showing that social choice functions based only on ordinal comparisons, rather than cardinal utility, will behave incoherently (unless they are dictatorial).
Dictatorships often crop up as degenerate cases or exceptions to theorems, e.g. Arrow's theorem. If there are at least three alternatives, dictatorship is the only ranked voting rule that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives.
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 is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a rational (non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting ...
Sen's proof, set in the context of social choice theory, is similar in many respects to Arrow's impossibility theorem and the Gibbard–Satterthwaite theorem. As a mathematical construct, it also has much wider applicability: it is essentially about cyclical majorities between partially ordered sets, of which at least three must participate in ...