Arrovian Aggregation in Economic Environments: How Much Should We Know About Indifference Surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference hypersurfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes "within the Edgeworth box" is not enough, and knowledge of substantially non-local information is necessary.social choice, preference aggregation, information, independence of irrelevant alternatives, indifference curves

Arrovian Aggregation in Economic Environments: How Much Should We Know About Indifference Surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference hypersurfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes "within the Edgeworth box" is not enough, and knowledge of substantially non-local information is necessary.social choice, preference aggregation, information, independence of irrelevant alternatives, indifference curves

Complete Characterization of Functions Satisfying the Conditions of Arrow\u27s Theorem

Arrow’s theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity), and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions, since non-strict preferences of the dictator are not necessarily followed. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow’s theorem, in the case of non-strict preferences, does not provide a complete characterization of all social welfare functions satisfying Transitivity, the Weak Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow’s theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow’s and Wilson’s result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Weak Pareto Principle). Additionally, we derive formulae for the number of functions satisfying these conditions

Aggregating Moral Preferences

Preference-aggregation problems arise in various contexts. One such context, little explored by social choice theorists, is metaethical. “Ideal-advisor” accounts, which have played a major role in metaethics, propose that moral facts are constituted by the idealized preferences of a community of advisors. Such accounts give rise to a preference-aggregation problem: namely, aggregating the advisors’ moral preferences. Do we have reason to believe that the advisors, albeit idealized, can still diverge in their rankings of a given set of alternatives? If so, what are the moral facts (in particular, the comparative moral goodness of the alternatives) when the advisors do diverge? These questions are investigated here using the tools of Arrovian social choice theory

Fair social decision under uncertainty and belief disagreements

This paper aims to address two issues related to simultaneous aggregation of utilities and beliefs. The first one is related to how to integrate both inequality and uncertainty considerations into social decision making. The second one is related to how social decision should take disagreements in beliefs into account. To accomplish this, whereas individuals are assumed to abide by Savage model’s of subjective expected utility, society is assumed to prescribe, either to each individual when the ex ante individual well-being is favored or to itself when the ex post individual well-being is favored, acting in accordance with the maximin expected utility theory of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989). Furthermore, it adapts an ex ante Pareto-type condition proposed by Gayer et al. (J Legal Stud 43:151–171, 2014), which says that a prospect Pareto dominates another one if the former gives a higher expected utility than the latter one, for each individual, for all individuals’ beliefs. In the context where the ex ante individual welfare is favored, our ex ante Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the individual set of priors being contained within the range of individual beliefs. However, when the ex post individual welfare is favored, the same Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the social set of priors containing only weighted averages of individual beliefs

The Pazner-Schmeidler Social Ordering: A Defense

It is shown that the Pazner-Schmeidler social ordering appears as a very natural solution to the problem of defining social preferences over distributions of a fixed bundle of divisible goods. The paper follows an approach to preference aggregation which relies only on interpersonally non-comparable preferences, and circumvents Arrow's impossibility by taking account of the shape of indifference curves. Social preferences can then be constructed and justified with fairness principles.social welfare, social choice, fairness, egalitarian-equivalencesocial welfare, public choice

Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem

Arrow's theorem implies that a social choice function satisfying Transitivity, the Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are allowed, a dictatorial social choice function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does not provide a complete characterization of all social choice functions satisfying Transitivity, the Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow's theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow's and Wilson's result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Pareto Principle). Additionally, we derive formulas for the number of functions satisfying these conditions.Comment: 11 pages, 1 figur

Social choice and the indexing dilemma

This paper distinguishes an index ordering and a social ordering function as a simple way to formalize the indexing problem in the social choice framework. Two main conclusions are derived. First, the alleged dilemma between welfarism and perfectionnism is shown to involve a third possibility, exemplified by the fairness approach to social choice. Second, the idea that an individual is better off than another whenever he has more (goods, functionings...) in all dimensions, which is known to enter in conflict with the Pareto principle, can be partly salvaged by adopting the fairness approach.social choice, indexing, Pareto, well-being

Two Criteria for Social Decisions

This paper studies the ethical underpinnings of two social criteria which are prominent in the literature dealing with the problem of evaluating allocations of several consumption goods in a population with heteregenous preferences. The Pazner-Schmeidler criterion (Pazner-Schmeidler 1978) and the Walrasian criterion (Fleurbaey and Maniquet 1996) are prima facie quite different. But it is shown here that these criteria are related to close variants of the fairness condition that an allocation is better when every individual bundle in it dominates the average consumption in another allocation. In addition, the results suggest that the Pazner-Schmeidler criterion can be viewed as the best extension of the Walrasian criterion to non-convex economies.social welfare, social choice, fairness