Lost in Translation: Social Choice Theory is Misapplied Against Legislative Intent

Several prominent scholars use results from social choice theory to conclude that legislative intent is meaningless. We disagree. We support our argument by showing that the conclusions in question are based on misapplications of the theory. Some of the conclusions in question are based on Arrow\u27s famous General Possibility Theorem. We identify a substantial chasm between what Arrow proves and what others claim in his name. Other conclusions come from a failure to realize that applying social choice theory to questions of legislative intent entails accepting assumptions such as legislators are omniscient and legislators have infinite resources for changing law and policy. We demonstrate that adding more realistic assumptions to models of social choice theory yields very different theoretical results-including ones that allow for meaningful inferences about legislative intent. In all of the cases we describe, important aspects of social choice theory were lost in the translation from abstract formalisms to real political and legal domains. When properly understood, social choice theory is insufficient to negate legislative intent

Social choice theory, game theory, and positive political theory

We consider the relationships between the collective preference and non-cooperative game theory approaches to positive political theory. In particular, we show that an apparently decisive difference between the two approachesthat in sufficiently complex environments (e.g. high-dimensional choice spaces) direct preference aggregation models are incapable of generating any prediction at all, whereas non-cooperative game-theoretic models almost always generate predictionis indeed only an apparent difference. More generally, we argue that when modeling collective decisions there is a fundamental tension between insuring existence of well-defined predictions, a criterion of minimal democracy, and general applicability to complex environments; while any two of the three are compatible under either approach, neither collective preference nor non-cooperative game theory can support models that simultaneously satisfy all three desiderata

Social Choice Theory and the Informational Basis Approach

For over a quarter of a century, the use of utility information based upon interpersonal comparisons has been seen as an escape route from the Arrow Impossibility Theorem. This paper critically examines this informational basis approach to social choice. Even with comparability of differences and levels, feasible social choice rules must be insensitive to a range of distributional issues. Also, the Pareto principle is not solely to blame for the inability to adopt rules combining utility and non-utility information: if the Pareto principle is not invoked then there is no way of combining utility and non-utility information in a ranking of states unless levels of utility are comparable; with only level comparability, information must be combined in restrictive ways and the notion of giving different independent weight to different considerations is ruled out. If informational bases are viewed as the restriction on information that is available, rather than a theoretical limit on information, then there exist methods to estimate richer informational structures and overcome some of these difficulties.

The Informational Basis of the Theory of Fair Allocation

The theory of fair allocation is often favourably contrasted with the social choice theory in the search for escape routes from Arrow's impossibility theorem. Its success is commonly attributed to the fact that it is modest in its goal vis-a-vis social choice theory, since it does not aspire for a full-fledged ordering of options, and settles with a subset of "fair" options. We show that its success may rather be attributable to a broadened informational basis thereof. To substantiate this claim, we compare the informational basis of the theory of fair allocation with the informational requirements of social choice theory.

Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory

A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetric under a transitive action with \E_p[f] = \eps and \E_q[f] = 1-\eps then $q-p \to 0$ as $n \to \infty$. Here \E_p denotes the product probability measure on $\{0,1\}^n$ where each coordinate takes the value $1$ independently with probability $p$. The fact that symmetric functions undergo sharp thresholds is important in the study of random graphs and constraint satisfaction problems as well as in social choice.In this paper we prove sharp thresholds for monotone functions taking values in an arbitrary finite sets. We also provide examples of applications of the results to social choice and to random graph problems. Among the applications is an analog for Condorcet's jury theorem and an indeterminacy result for a large class of social choice functions

Inductive Reasoning in Social Choice Theory

The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations (each one consisting of a profile and the associated social ordering) the criteria verified in the implicit aggregation procedure. This inference process, which extracts intensional from extensional information can be seen as an exercise in “qualitative statistics”.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Auday, Marcelo. Universidad Nacional del Sur; Argentin

Introduction to social choice and welfare

Social choice theory is concerned with the evaluation of alternative methods of collective decision-making, as well as with the logical foundations of welfare economics. In turn, welfare economics is concerned with the critical scrutiny of the performance of actual and/or imaginary economic systems, as well as with the critique, design and implementation of alternative economic policies. The Handbook of Social Choice and Welfare, which is edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. This paper is written as an extensive introduction to the Handbook with the purpose of placing the broad issues examined in the two volumes in better perspective, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory.social choice theory, welfare economics, socialist planning controversy, social welfare function, Arrovian impossibility theorems, voting schemes, implementation theory, equity and justice, welfare and rights, functioning and capability, procedural fairness