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This paper is concerned with the "General Possibility Theorem" of Dr. K. J. Arrow. Since the theorem is certainly elegant and probably important, it is proper as well as convenient to refer to it from this point on as Arrow's theorem. The theorem deals with the problem of discovering a rule by which social preferences can be constructed from individual preferences. Such a rule, or social welfare function, gives a social ordering of alternatives of any kind for every possible arrangement of the corresponding individual orderings. Arrow's theorem declares that no social welfare function exists that satisfies those conditions that most of us would consider essential to a satisfactory rule. The outcome is something of a shock to preconceptions.In what follows two aspects of Arrow's theorem are considered. In the early part of the paper the theorem as such is examined. A brief and informal statement of Arrow's argument is followed by a formal statement of the conditions on which the argument depends. A proof of the theorem is offered that seems to be rather more naturally constructed than the original. A set of conditions is proposed (derived from Arrow's proof) that is weaker than the original set, that seems to be at least as plausible, and that leads to the same conclusion by a short and direct route. In the later part of the paper, methods of circumventing the theorem (there seems to be no way of removing it) are explored.

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.

The circumstances of the author's discovery of the median voter theorem and the steps which led from there to his Theory of Committees and Elections are set out. His theory is presented in the form of the `statistical thesis' that the best choice procedure selects the option which `on average' is highest on the committee members' schedules. As there is more than one concept of average, so there is more than one acceptable committee procedure. The author's way of proceeding is compared and contrasted with Arrow's.

AbstractThe paper considers Mackie's defence of 'populist' democracy against the critique offered by Riker and the Rochester School. Riker has two arguments against populism: first that Arrow's theorem shows there is no such thing as the general will, second, that once we have chosen a social decision mechanism the results may not represent the true wishes of the population since people may vote strategically. Mackie argues Arrow's theorem is misleading since the independence condition is not itself substantively rational, and that manipulation never actually occurs. The paper shows that independence is needed for interpretation and prediction, and whilst Arrow's strong condition may not be 'substantively rational', examples show that no single decision mechanism, even Mackie's favoured Borda count is obviously superior. It then argues that every election can, in Arrow's terms, be considered as manipulated – though there is nothing substantively wrong in that. The paper ends by pointing out that in the absence of complete information market outcomes are also similarly manipulated.

Examined are the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences, which assume that each person has a most preferred alternative in a euclidean space, & that alternatives are ranked according to their euclidean distance from this point. The result is that if one imposes K. J. Arrow's (Social Choice and Individual Values, 2nd edition, New Haven: Yale U Press, 1963) conditions of collective rationality, IIA, & the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by A. Gibbard ("Manipulation of Voting Schemes: A General Result," Econometrica, 1973, 41, 587-601) & M. A. Satterthwaite ("Strategy-Proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions," Journal of Economic Theory, 1975, 10, 187-217) of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences, this result has been previously shown to not be true. This finding identifies a significant difference between the Arrow & Gibbard-Satterthwaite problems. 7 Figures, 18 References. Modified HA.

This paradox of voting in Arrow's theorem has hardly any application to voting in the real world. Arrow, in introducing his theorem, says specifically that it does not apply in those cases in which individuals do not vote according to their elementary preferences, but accept payment of some sort to vote against them. Since log-rolling is usual in most democratic legislatures, the theorem does not apply.

THE PARADOX OF VOTING PRESENTED IN ARROW'S THEOREM HAS HARDLY ANY APPLICATION TO VOTING IN THE REAL WORLD. IN INTRODUCING HIS THEOREM, ARROW SAYS SPECIFICALLY THAT IT DOES NOT APPLY IN THOSE CASES IN WHICH INDIVIDUALS DO NOT VOTE ACCORDING TO THEIR ELEMENTARY PREFERENCES BUT ACCEPT PAYMENT OF SOME SORT TO VOTE AGAINST THEIR TRUE INCLINATIONS. SINCE LOG-ROLLING IS COMMON IN MOST DEMOCRATIC LEGISLATURES, THE THEOREM DOES NOT APPLY.

Covers topics such as: models of economic exchange and production, uncertainty, optimality, public goods, social improvement criteria, life and death choices, majority voting, Arrow's theorem, and theories of implementation and mechanism design. This book aims to make value judgments about economic and political mechanisms

1.A Dictator Must Always Exist -- 2.Arrow's Theorem is a Powerful Tool for Understanding Many Social Phenomena -- 3.Catherine the Great and Genghis Khan: Power has no Gender -- 4.Some Open Problems for a General Mathematical Theory of Social Structures -- 5.Phenomenology of Leadership -- 6.Phenomenology of Dictatorship