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"This book develops John Dewey's broad conception of social conflict as a natural process of discovery and preference adjustment, resolving Kenneth Arrow's famous theorem of the impossibility of ordering diverse preferences through voting. It addresses the nature and resolution of today's urgent problems and political polarization"--

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.

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.

IN THIS NOTE THE AUTHORS STUDY DIFFERENT METHODS OF AGGREGATION OF PREFERENCES MET ON THE OCCASION OF ELECTIONS. THROUGH A SIMPLE GEOMETRICAL REPRESENTATION, THEY ANALYSE SEVERAL OF THEIR PROPERTIES, IN PARTICULAR THOSE LINKED TO ARROW'S THEOREM FOR ORDINAL RANKINGS; THEY PURSUE THIS DISCUSSION IN THE CASE OF CARDINAL RANKINGS, THE QUALITIES OF WHICH CONVINCE US OF THE USEFULNESS OF EXPERIENCING THEIR INTRODUCTION IN REAL BALLOTS.

A comparatively short proof of the following theorems is given: If a social choice function, which in any voting situation selects only one alternative as the winning alternative, has at least three posible outcomes & is not dictatorial, then it is subject to strategic manipulation by single individuals. This theorem has been proved independently by A. Gibbard ("Manipulation of Voting Schemes: A General Result," Econometrica, 1973, 41, 587-601) & M. 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). The new proof of the theorem is based on a version of Arrow's impossibility theorem shown by B. Hansson ("Voting and Group Decision Functions," Synthese, 1969, 20, 526-537). AA.

We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives & to offer new interpretations for pairwise voting. The source of the problems -- an unanticipated loss of available information -- also explains a variety of other phenomena, such as Simpson's paradox (a statistical paradox in which the behavior of the "parts" disagrees with that of the "whole") & Arrow's theorem from social choice. 6 Tables, 4 Figures, 1 Appendix, 23 References. Adapted from the source document.

Kenneth Arrow's treatment of social choice ("A Difficulty in the Concept of Social Welfare," Journal of Political Economy, 1950, 58, 328-346) led to the formulation of his 'Impossibility Theorem', according to which it would be impossible for a society to ethically consider the preferences of all its members in formulating policies. By making certain changes in Arrow's assumptions, the contradictions he encountered can be avoided. Arguments are presented which arrive at a "social choice procedure that will translate judgments of preference priority into a social ordering." A determination of preference priority leads to a theorem very similar to John Rawls' difference principle (A THEORY OF JUSTICE, Cambridge, Mass: 1971) which recognizes the moral priority of those in the worst social position. Appendix. J. N. Mayer.

Arrow's paradox, important to the foundation of social choice theory & individual choice theory, was solved by reducing Arrow's rationality assumptions to acyclicity. Another paradox is presented which requires the abandonment of acyclicity as well. The construction of the paradox allows for certain intransitivities of individual indifference resulting from less than n significant one. The following are assumed: (1) the Citizens' intransitive weak preference, (2) the Strong Pareto Principle, & (3) Ternary acyclicity. The acceptance of the reasonableness of assumptions 1 & 2, forces the rejection of assumption 3; all of which is a fundamental change in the theory of social choice. S. Lupton.

If the class of admissible preference orderings is restricted in a manner appropriate for economic & political models, then K. J. Arrow's (Social Choice and Individual Values, New York: Wiley, 1963) impossibility theorem for social welfare function continues to be valid. Specifically, if the space of alternatives is R****, n(greater than or equal to) 3, where each dimension represents a different public good, & if each person's preferences are restricted to be convex, continuous, & strictly monotonic, then no social welfare function exists that satisfies unanimity, independence of irrelevant alternatives, & nondictatorship. 1 Figure. HA.

"Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections: Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague-Grundy theorem and Arrow's impossibility theorem; Uses an integrative approach to probability, game, and social choice theory; Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies; Contains numerous exercises and examples of varying levels of difficulty; Requires only a high school mathematical background"--