arrow paradox See ZENO’S PARADOXES. Arrow’s paradox, also called Arrow’s (impossibility) theorem, a major result in social choice theory, named for its discoverer, economist Kenneth Arrow. It is intuitive to suppose that the preferences of individuals in a society can be expressed formally, and then aggregated into an expression of social preferences, a social choice function. Arrow’s paradox is that individual preferences having certain well-behaved formalizations demonstrably cannot be aggregated into a similarly well-behaved social choice function satisfying four plausible formal conditions: (1) collective rationality – any set of individual orderings and alternatives must yield a social ordering; (2) Pareto optimality – if all individuals prefer one ordering to another, the social ordering must also agree; (3) non-dictatorship – the social ordering must not be identical to a particular individual’s ordering; and (4) independence of irrelevant alternatives – the social ordering depends on no properties of the individual orderings other than the orders themselves, and for a given set of alternatives it depends only on the orderings of those particular alternatives. Most attempts to resolve the paradox have focused on aspects of (1) and (4). Some argue that preferences can be rational even if they are intransitive. Others argue that cardinal orderings, and hence, interpersonal comparisons of preference intensity, are relevant. See also DECISION THEORY, SOCIAL CHOICE THEOR. A.N.