Measurement Theory and the Foundations of Utilitarianism

Harsanyi used expected utility theory to provide two axiomatizations of weighted utilitarian rules. Sen (and later, Weymark) has argued that Harsanyi has not, in fact, axiomatized utilitarianism because he has misapplied expected utility theory. Specifically, Sen and Weymark have argued that von Neumann-Morgenstern expected utility theory is an ordinal theory and, therefore, any increasing transform of a von Neumann-Morgenstern utility function is a satisfactory representation of a preference relation over lotteries satisfying the expected utility axioms. However, Harsanyi's version of utilitarianism requires a cardinal theory of utility in which only von Neumann-Morgenstern utility functions are acceptable representations of preferences. Broome has argued that von Neumann-Morgenstern expected utility theory is cardinal in the relevant sense needed to support Harsanyi's utilitarian conclusions. His basic point is that a preference binary relation is not a complete description of preferences in the von Neumann-Morgenstern theory. Rather, the preference relation needs to be supplemented by a binary operation, and it is this operation that makes the theory cardinal. Broome does not provide a formal argument in support of this conclusion. In this article, measurement theory is used to critically evaluate Broome's claims. It is shown that the criticisms of Harsanyi's theory by Sen and Weymark can be extended to the more complete description of expected utility theory that is obtained by using the mixture operators that appear in von Neumann and Morgenstern's original description of expected utility theory in addition to a preference relationexpected utility, utilitarianism, von Neumann-Morgenstern, Harsanyi

Social Choice with Analytic Preferences

A social welfare function is a mapping from a set of profiles of individual preference orderings to the set of social orderings of a universal set of alternatives. A social choice correspondence specifies a nonempty subset of the agenda for each admissible preference profile and each admissible agenda. We provide examples of economic and political preference domains for which the Arrow social welfare function axioms are inconsistent, but whose choice-theoretic counterparts (with nondictatorship strengthened to anonymity) yield a social choice correspondence possibility theorem when combined with a natural agenda domain. In both examples, agendas are compact subsets of the nonnegative orthant of a multidimensional Euclidean space. In our first possibility theorem, we consider the standard Euclidean spatial model used in many political models. An agenda can be interpreted as being the feasible vectors of public goods given the resource constraints faced by a legislature. Preferences are restricted to be Euclidean spatial preferences. Our second possibility theorem is for economic domains. Alternatives are interpreted as being vectors of public goods. Preferences are monotone and representable by an analytic utility function with no critical points. Convexity of preferences can also be assumed. Many of the utility functions used in economic models, such as Cobb-Douglas and CES, are analytic. Further, the set of monotone, convex, and analytic preference orderings is dense in the set of continuous, monotone, convex preference orderings. Thus, our preference domain is a large subset of the classical domain of economic preferences. An agenda can be interpreted as the set of feasible allocations given an initial resource endowment and the firms' production technologies. To establish this theorem, an ordinal version of the Analytic Continuation Principle is developed.

Multidimensional generalized Gini indices.

The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.Generalized Gini; multidimensional inequality

Candidate Stability and Nonbinary Social Choice

A desirable property of a voting procedure is that it be immune to the strategic withdrawal of a candidate for election. Dutta, Jackson, and Le Breton (Econometrica, 2001) have established a number of theorems that demonstrate that this condition is incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of these impossibility theorems.Une des propriétés désirables d’une procédure de vote est qu’elle doit être exempte de retrait stratégique d’un candidat à l’élection. Duttu, Jackson et Le Breton (Econometrica, 2001) ont établi des théorèmes démontrant que cette propriété est incompatible avec certaines propriétés désirables de procédures de vote. Cet article montre que la généralisation non binaire du théorème d’Arrow par Grether et Plott peut être utilisée pour faire une démonstration assez simple de deux de ces théorèmes d’impossibilité

Social Choice: Recent Developments

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic modelling has played a prominent role: Arrovian social choice theory on economic domains, variable-population social choice, strategy-proof social choice, and axiomatic models of resource allocation

Shared destinies and the measurement of social risk equity

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2008.htmClassification JEL : D63, D81.Documents de travail du Centre d'Economie de la Sorbonne 2008.69 - ISSN : 1955-611XThe evaluation of social risk equity for alternative probability distributions over the potential sets of fatalities is analyzed axiomatically. Fishburn and Straffin [Equity considerations in public risks valuation, Operatons Research 37 (1999), 229-239] have identified a necessary and sufficient condition for two social risk distributions to be judged to be socially indifferent whenever their associated distributions of risk of death for individuals and for the number of fatalities are the same. It is argued that this approach does not permit society to exhibit any concern for the number of people an individual perishes with. A weakening of the Fishburn-Straffin condition that is compatible with a concern for shared destinies is proposed.Nous proposons une analyse axiomatique de l'évaluation de l'exposition collective à un risque de décès. Il s'agit plus précisément de comparer, en termes d'équité, différentes distributions de probabilité de décès pour l'ensemble des sous-groupes de la population. Fishburn and Straffin [Equity considerations in public risks valuation, Operatons Research 37 (1999), 229-239] ont identifié une condition nécessaire et suffisante pour que deux risques sociaux soient jugés également équitables dès lors qu'ils conduisent d'une part à des probabilités individuelles de décès identiques, et d'autre part aux même distributions de probabilité sur le nombre de décès. Nous montrons qu'une telle approche ne permet pas de prendre en compte l'importance que peut avoir le fait de partager son destin avec un plus ou moins grand nombre d'autres personnes. Nous proposons un affaiblissement de la condition de Fishburn et Straffin qui permet de tenir compte de l'influence de la communauté de destin dans l'évaluation d'un risque social

An axiomatic characterization of the MVSHN group fitness ordering

In order to analyze a unicellular-multicellular evolutionary transition, a multicellular organism is identified with the vector of viabilities and fecundities of its constituent cells. The Michod–Viossat–Solari–Hurand–Nedelcu index of group fitness for a multicellular organism is a function of these cell viabilities and fecundities. The MVSHN index has been used to analyze the germ-soma specialization and the fitness decoupling between the cell and organism levels that takes place during the transition to multicellularity. In this article, social choice theory is used to provide an axiomatic characterization of the group fitness ordering of vectors of cell viabilities and fecundities underlying the MVSHN index

Extensive Social Choice and the Measurement of Group Fitness in Biological Hierarchies

Extensive social choice theory is used to study the problem of measuring group fitness in a two-level biological hierarchy. Both fixed and variable group size are considered. Axioms are identified that imply that the group measure satisfies a form of consequentialism in which group fitness only depends on the viabilities and fecundities of the individuals at the lower level in the hierarchy. This kind of consequentialism can take account of the group fitness advantages of germ-soma specialization, which is not possible with an alternative social choice framework proposed by Okasha, but which is an essential feature of the index of group fitness for a multicellular organism introduced by Michod, Viossat, Solari, Hurand, and Nedelcu to analyze the unicellular-multicellular evolutionary transition. The new framework is also used to analyze the fitness decoupling between levels that takes place during an evolutionary transition

Constraints on profit income distribution and production efficiency in private ownership economies with Ramsey taxation

Author's draft published as discussion paper by University of Exeter Department of Economics. The original publication is available at www.springerlink.comIn economies with Ramsey taxation, decreasing returns to scale, and private ownership, we show that second-best production efficiency is desirable when the grouping of private firms induced by the profit taxation power of the government is at least as fine as the grouping of firms induced by the institutional rules of profit distribution in the economy. The classic results of Dasgupta and Stiglitz [1972] (of firm-specific profit taxation) and Diamond and Mirrlees [1971] and Guesnerie [1995] (of uniform one-hundred percent profit taxation) follow as special cases of our model. Moreover, second-best analysis shows that optimal profit taxation is a substitute for optimal intermediate input taxation. In smooth economies, proportional, lump-sum, and affine modes of profit taxation are equivalent. We rework Mirrlees [1972] counterexample, which is posed in the context of a non-smooth economy, to show that second-best production efficiency continues to remain desirable under an affine structure of profit taxation