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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 ...
Arrow's Theorem [1]: The 3 conditions of the constitution imply a dictator who prevails as to the social choice whatever that individual's preference and those of all else. An alternate statement of the theorem adds the following condition to the above: 4. Nondictatorship D: No voter in the society is a dictator.
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between and should not depend on the quality of a third, unrelated outcome . There are several different variations of this axiom, which are generally equivalent under mild conditions.
^May, Kenneth O. 1952. "A set of independent necessary and sufficient conditions for simple majority decisions", Econometrica, Vol. 20, Issue 4, pp. 680–684. JSTOR 1907651; ^ Mark Fey, "May’s Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.; ^ Goodin, Robert and Christian List (2006). "A conditional defense of plurality rule ...
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. [1] Social choice studies the behavior of different mathematical procedures ( social welfare functions ) used to combine individual preferences into a coherent whole.
Arrow's theorem is not related to strategic voting, which does not appear in his framework, [3] [1] though the theorem does have important implications for strategic voting (being used as a lemma to prove Gibbard's theorem [15]). The Arrovian framework of social welfare assumes all voter preferences are known and the only issue is in ...
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory.The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters: for example there can be rock-paper-scissors scenario where a majority of voters will prefer ...
[1] [2] [3] 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 ...