through the votes of others under the constitution. The result generalizes and deepens the voting paradox to any voting rule satisfying the conditions, however complex or comprehensive. The 1963 edition includes an additional chapter with a simpler proof of Arrow's Theorem and corrects an earlier point noted by Blau. It also elaborates on advantages of the conditions and cites studies of Riker and Dahl that as an empirical matter intransitivity of the voting mechanism may produce unsatisfactory inaction or majority opposition. These support Arrow's characterization of a constitution across possible votes (that is, collective rationality) as "an important attribute of a genuinely democratic system capable of full adaptation to varying environments" (p. 120). The theorem might seem to have unravelled a skein of behavior-based social-ethical theory from Adam Smith and Bentham on. But Arrow himself expresses hope at the end of his Nobel prize lecture that, though the philosophical and distributive implications of the paradox of social choice were "still not clear," others would "take this paradox as a challenge rather than as a discouraging barrier." The large subsequent literature has included reformulation to extend, weaken, or replace the conditions and derive implications. In this respect Arrow's framework has been an instrument for generalizing voting theory and critically evaluating and broadening economic policy and social choice theory. See also Arrow's impossibility theorem Kenneth Arrow, Section 1 (the theorem and a distributional difficulty of intransitivity + majority rule) Abram Bergson Buchanan and Tullock, The Calculus of Consent: Logical Foundations of Constitutional Democracy Independence of irrelevant alternatives Pareto efficiency, strong and weak Path dependence, contrasted in Arrow with path independence, which a social ordering assures Political argument Public choice theory Social choice theory Social welfare function Rule according to higher law Utilitarianism Voting paradox Voting system Welfare economics Welfarism JEL D71 by scrolling down for Social Choice Notes References Kenneth J. Arrow, 1951, 2nd ed., 1963, 3rd ed., 2012. Social Choice and Individual Values, Yale University Press. _, 1983. Collected Papers of Kenneth J. Arrow, v. 1, Social Choice and Justice. Description and chapter-preview links. Harvard University Press. _, 1987. “Arrow’s Theorem," The New Palgrave: A Dictionary of Economics, v. 1, pp. 124–26. _, 2008. "Arrow's theorem." The New Palgrave Dictionary of Economics, 2nd Edition Abstract. Amartya K. Sen, 1970 [1984]. Collective Choice and Social Welfare (description), ch. 1–7.1. . . Michael Morreau, 2014. "Arrow's Theorem", The Stanford Encyclopedia of Philosophy (Winter