An Introduction to Arrovian Social Welfare Functions on Economic and Political Domains

A social welfare function assigns a social preference ordering to each admissible profile of individual preference orderings of a set of alternatives. Arrow (1963) required a social welfare function to satisfy the following list of axioms: Weak Pareto (if everyone strictly prefers one alternative to a second alternative, then so does society), Binary Independence of Irrelevant Alternatives (the social preference for a pair of alternatives depends only on the individual preferences for this pair), and Nondictatorship (nobody has his or her strict preferences always respected). Arrow’s Theorem demonstrates that these axioms are inconsistent if the domain of admissible profiles of individual preference orderings is unrestricted and if there are at least three alternatives being ranked.2

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