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.
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.
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.
The impossibility theorem developed by Kenneth Arrow has implications for both rationality and morality in political thought. Transitivity in a collective ordering can be assured only with a decisive set, but this outcome is acknowledged as morally undesirable. The alternatives exhibited by the theorem thus seem to require a choice between rationality and morality. But exit routes can be cut out of this dilemma with the idea of a conditional ordering, one where warranting factors attach to a ranking of alternatives. Conditional orderings form two senses of collective rationality. One is represented by compound directives, which avoid the rational problems of the theorem by warranting local orderings. The second is moral fusion, which requires a reasoned dominance in collective outcomes. These two forms of conditional rationality put into relief the restricted scope of the composition rules and individualism of Arrow's theorem, and suggest alternative relationships of individual and social whole.
Kenneth J. Arrow was one of the most important intellectuals of the twentieth century, and his "impossibility theorem" is arguably the starting point of modern, axiomatic social choice theory. In this review, we begin with a brief discussion of Arrow's theorem and subsequent work that extended the result. We then discuss its implications for voting and constitutional systems, including a number of seminal results—both positive and negative—that characterize what such systems can accomplish and why. We then depart from this narrow interpretation of the result to consider more varied institutional design questions such as apportionment and geographical districting. Following this, we address the theorem's implications for measurement of concepts of fundamental interest to political science such as justice and inequality. Finally, we address current work applying social choice concepts and the axiomatic method to data analysis more generally.
This paper analyzes the implications of social choice theory for the study of world politics. A view of the world system as a social choice mechanism leads to the observation that the outcomes of world politics are determined neither by structure nor by preferences alone, but rather by their interaction. Structural change occurs only when the actors cannot achieve their preferences through the current system. Three particular social choice mechanisms are analyzed to determine which conditions of Arrow's theorem they violate. The argument is illustrated by examining two salient theoretical works, Waltz's Theory of International Politics and Gilpin's War and Change in World Politics. The critique of Waltz illustrates that structure alone cannot determine outcome; the critique of Gilpin examines how structural change occurs in world politics and underlines the importance of preferences in such changes.
Amartya Sen has recently suggested that certain issues which arise in the application of the capability approach can be seen in terms of social choice. This article explores certain connections and tensions between Kenneth Arrow's celebrated discussion of social choice and the capability approach while focusing on one central link: pluralism. Given the variety of values people hold, substantive issues which arise in the application of the capability approach can be seen as social choice problems. Seeing them in this way helps to explain some of Sen's suggestions about applying the approach in the light of an analogue of Arrow's theorem. However, it also poses a potential problem because of the focus on preferences in social choice theory, given that the capability approach is motivated in part by problems which `adaptive preferences' raise for `utility'-based views. In this article, it is argued that Sen's writings about public reasoning allow him to address this problem to some degree. The reading underlying this argument clarifies issues about the relationship between the individual and society in his approach. It also illuminates the extent of Sen's debt to John Rawls's writings on `public reason', while clarifying some points on which Sen and Rawls diverge.
Antonio Quesada (Public Choice 130:395-400, 2007) argues that a dictator has no more than two to three times the 'average power' of a non-dictatorial voter. If Quesada is correct, then his argument has major consequences for social choice theory; for instance, it warrants reconsidering the significance of Arrow's Theorem. If Quesada is incorrect, however, then his position is dangerously misleading. This paper argues that Quesada is wrong. His argument depends on his own formal account of power, an account that is implausible because it disregards a basic insight common to the standard characterisations of voting power: the idea that one has power over an outcome to the extent that one is able to change that outcome. Claims about power have a counterfactual component; to assert that an individual actually has determined an outcome is also to make an assertion about what would have been the case had that individual acted differently. We can employ David Lewis's influential account of counterfactuals to show, contra Quesada, that in a dictatorship, non-dictatorial individuals and groups cannot possibly determine a social preference. In short, Quesada is fundamentally mistaken about power, and thus also about the distribution of power in a dictatorship. Adapted from the source document.
