Utilitarian Aggregation of Beliefs and Tastes

Economic Theory, 2000

We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs.

Journal of Mathematical Economics, 87 (2020) 77-113, 2020

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.

SSRN Electronic Journal, 1998

Discussions over the years with John Broome, Claude d'Aspremont, Philippe Mongin, and John Roemer on the subject of Harsanyi's theorem have been particularly useful in preparing this article. Our research has been generously supported by the Social Sciences and Humanities Research Council of Canada.

Theory and Decision, 2022

Following Aumann (1987), we introduce the notion of comprehensive state of the world, which, unlike Savage's notion of state, describes a consequence. Comprehensive states result in Savage's model when an act is fixed. We study desirability, which is a binary relation defined on events, that is, subsets of comprehensive states. One of our main results shows that a desirability relation that satisfies certain axioms can be represented by probability and utility, by taking a conditional expected utility. Despite the difference of domains, some of our axioms are analogous to Savage's axioms. Some other axioms resemble axioms of Bolker for binary relations on events in a consequenceless model, which guarantee representation by ratio of two measures. Our axioms allow for endogenous derivation of consequences from a desirability relation, in contrast to Savage's model and similar models in which consequences, which are primitives of the theory, are assumed exogenously. The representation is not unique and we characterize all probability-utility pairs that represent a given desirability relation. We show that when desirability relations for a large set of acts satisfy some consistency axioms, then there exists a single pair that represents all of them.

The SAGE Handbook of the Philosophy of Social Sciences, 2011

The Economic Journal, 2018

We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions. We are particularly grateful to Luigi Balletta, Ludovic Renou, three anonymous referees, and the editor for comments on earlier versions of this paper and for important references. Gilboa gratefully acknowledges support from ISF Grants 204/13, 704/15, the Foerder Foundation, ERC Grant 269754, and Investissements d'Avenir ANR-11-IDEX-0003 / Labex ECODEC No.

Journal of Economic Theory, 2012

We provide an axiomatization of expected equally-distributed equivalent-utility social welfare functions in the context of Harsanyi's impartial observer theorem. For this family of social welfare functions, we show what additional axiom is necessary and sufficient for the observer to exhibit aversion to ex post inequality. We also relate this axiomatization to our axiomatization in a companion paper of generalized utilitarian social welfare functions. Given certain richness assumptions, the only social welfare functions that belong to both families are the utilitarian.

Journal of Mathematical Economics, 2009

Savage's expected utility theory orders acts by the expectation of the utility function for outcomes over states. Therefore, preference between acts depends only on the utilities for outcomes and the probability distribution of states. When acts have more than finitely many possible outcomes, then utility is bounded in Savage's theory. This paper explores consequences of allowing preferences over acts with unbounded utility. Under certain regularity assumptions about indifference, and in order to respect (uniform) strict dominance between acts, there will be a strict preference between some pairs of acts that have the same distribution of outcomes. Consequently in these cases, preference is not a function of utility and probability alone.

2015

We consider a decision maker that holds multiple preferences simultaneously, each with different strengths described by a probability distribution. Faced with a subset of available alternatives, the preferences held by the individual can be in conflict. Choice results from an aggregation of these preferences. We assume that the aggregation method is monotonic: improvements in the position of alternative x cannot displace x if it were originally the choice. We show that choices made in this manner can be represented by context-dependent utility functions that are monotonic with respect to a measure of the strength of each alternative among those available. Using this representation we show that any generic monotonic rule can generate an arbitrary choice function as we vary the distribution of preferences. Domain restrictions on the set of preferences (e.g. dual motivation models) or consistency restrictions on the aggregator across choice sets reduce the set of admissible behaviors. Applications to positive models of individual decision making with context effects and social choice are discussed.

Social Science Research Network, 2017

We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions. We are particularly grateful to Luigi Balletta, Ludovic Renou, and an anonymous referee for comments on earlier versions of this paper and for important references. Gilboa gratefully acknowledges support from ISF Grants 204/13, 704/15, the Foerder Foundation, and ERC Grant 269754.