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In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow's theorem, all voting methods must be seriously flawed. Arrow's theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow's result. Parallel to Arrow's ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow's theorem, but rather from restrictions imposed on voters' expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior.

This book discusses collective decision making from the perspective of social choice and game theory. The chapters are written by well-known scholars in the field. The topics range from Arrow's Theorem to the Condorcet and Ostrogorski Paradoxes, from vote distributions in the European Council to influence processes and information sharing in collective decision making networks; from cardinal utility to restricted domains for social welfare functions; from rights and game forms to responsibility in committee decision making; and from dueling to bargaining. The book reflects the richness and diversity of the field of collective decision making and shows the usefulness and adequacy of social choice and game theory for the study of it. It starts with typical social choice themes like Arrow's Theorem and ends with typical game theoretical topics, like bargaining and interval games. In between there is a mixture of views on collective decision making in which both social choice and game theoretic aspects are brought in. The book is dedicated to Harrie de Swart, who organized the well-known Social Choice Colloquia at the University of Tilburg in the Netherlands.

Abstract. In this note we study different methods of aggregation of preferences met on the occasion of elections. Through a simple geometrical representation, we analyse several of their properties, in particular those linked to Arrow's theorem for ordinal rankings; we 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.

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.

Voting -- Two candidates -- Social choice functions -- Criteria for social choice -- Which methods are good? -- Arrow's theorem -- Variations on the theme -- Apportionment -- Hamilton's method -- Divisor methods -- Criteria and impossibility -- The method of Balinski and Young -- Deciding among divisor methods -- History of apportionment int he United States -- Conflict -- Strategies and outcomes -- Chance and expectation -- Solving zero-sum games -- Conflict and cooperation -- Nash equilibria -- The prisoner's dilemma -- The electoral college -- Weighted voting -- Whose advantage?

The concept of the General Will has been criticized as being either tyrannical or empirically unattainable. From a social choice perspective, Riker (1982) and others have merged the substance of both perspectives. The new argument maintains that Arrow's Theorem and similar impossibility results imply that the General Will is both dangerous and "intellectually absurd." While not denying the relevance of the collective choice literature, it is argued that such apocalyptic conclusions are premature.

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.

"Rational Choice Theory in Political Decision Making" published on by Oxford University Press.

The sociological explanation of altruistic behaviour often encounters serious difficulties. This essay attempts to solve the altruism enigma through the presentation of an alternative explanation to Arrow's Possibility Theorem as well as to Berlin's serious objections to rational calculus in political behaviour. Bestowing charisma and/or sacredness to certain values often proves the solution to the puzzle by providing a rational criterion for action which cancels out other criteria and calculations. The Possibility Theorem which is put forward here solves the problem of the rationality of the supposedly irrational in rational choice situations and dilemmas. The Possibility Theorem is a contribution to the issue of the rationality of charisma and, therefore, to the analytical explanation of altruistic behaviour. ; La explicación sociológica del altruismo presenta serias dificultades. El presente ensayo propone resolver el enigma del altruismo mediante la presentación de una explicación alternativa al Teorema de Imposibilidad de Arrow así como a las objeciones de Berlin al cálculo racional en política. La atribución de carisma o sacralidad a ciertos valores genera, frecuentemente, la solución. Tal atribución suministra un criterio racional de acción que supera y descarta otros cálculos. El Teorema de Posibilidad que aquí se postula resuelve el problema de la racionalidad de lo supuestamente irrracional en las trías o elecciones racionales de conducta. El Teorema propuesto es una aportación a la cuestión de la racionalidad del carisma y, por ende, a la explicación analítica del altruismo.

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 and 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") and Arrow's theorem from social choice.

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.