Utilitarianism with Prior Heterogeneity

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2014.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2014.49 - ISSN : 1955-611XHarsanyi's axiomatic justification of utilitarianism is extended to a framework with subjective and heterogenous priors. Contrary to the existing literature on aggregation of preferences under uncertainty, society is here allowed to formulate probability judgements, not on the actual state of the world as individuals do, but rather on the opinion they each have on the actual state. An extended Pareto condition is then proposed that characterizes the social utility function as a convex combination of individual ones and the social prior as the independent product of individual ones.La justification axiomatique de l'utilitarisme d'Harsanyi est généralisée à un cadre dans lequel les croyances individuelles sont subjectives et hétérogènes. A l'inverse de la littérature existante sur l'agrégation de préférences en environnement incertain, la société formule des jugements de probabilité, non pas sur le véritable état du monde - ce que les individus font -, mais plutôt sur les opinions qu'entretiennent les individus à propos du véritable état du monde. Une forme étendue de la condition de Pareto est alors proposée et il est montré qu'elle caractérise l'utilité sociale en tant que combinaison convexe des utilités individuelles et la probabilité sociale en tant que produit indépendant des probabilités individuelles

Expected Utility without Parsimony

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2014.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2014.48 - ISSN : 1955-611XThis paper seeks to interpret observable behavior and departures from Savage's model of Subjective Expected Utility (SEU) in terms of knowledge and belief. It is shown that observable behavior displays sensitivity to ambiguity if and only if knowledge and belief disagree. In addition, such an epistemic interpretation of ambiguity leads to dynamically consistent extensions of non-SEU preferences.Ce papier cherche à interpréter le comportement observable d'un individu, et notamment les violations du modèle d'espérance subjective d'utilité (SEU), en termes de savoir et de croyance. Il est montré que le comportement observable révèle de la sensitivité à l'ambiguïté si et seulement si savoir et croyance diffèrent. De plus, une telle interprétation épistémique de l'ambiguïté mène à des extensions dynamiquement cohérentes des préférences non-SEU

Dynamic Consistency and Expected Utility with State Ambiguity

While models of ambiguity are reputed to generate a basic tension between dynamic consistency and the Ellsberg choices, this paper identifies a third implicit ingredient of this tension, namely the parsimony rule, which enforces each state of nature to encode a well-defined unique observation. This paper then develops nonparsimonious interpretations of the state space to make the Ellsberg choices compatible with both expected utility and dynamic consistency. The state space may contain nonobservable states: a state is allowed to encode more than one observation, a pattern called state ambiguity. The presence of such ambiguous states motivates an explicit distinction between the decision-maker and the theory-maker, the latter designing the state space and eliciting the former's preferences

Infinite Supermodularity and Preferences

This chapter studies the ordinal content of supermodularity on lattices. This chapter is a generalization of the famous study of binary relations over finite Boolean algebras obtained by Wong, Yao and Lingras. We study the implications of various types of supermodularity for preferences over finite lattices. We prove that preferences on a finite lattice merely respecting the lattice order cannot disentangle these usual economic assumptions of supermodularity and infinite supermodularity. More precisely, the existence of a supermodular representation is equivalent to the existence of an infinitely supermodular representation. In addition, the strict increasingness of a complete preorder on a finite lattice is equivalent to the existence of a strictly increasing and infinitely supermodular representation. For wide classes of binary relations, the ordinal contents of quasisupermodularity, supermodularity and infinite supermodularity are exactly the same. In the end, we extend our results from finite lattices to infinite lattices

Subjective expected utility representations for Savage preferences on topological spaces

In many decisions under uncertainty, there are technological constraints on both the acts an agent can perform and the events she can observe. To model this, we assume that the set S of possible states of the world and the set X of possible outcomes each have a topological structure. The only feasible acts are continuous functions from S to X, and the only observable events are regular open subsets of S. In this environment, we axiomatically characterize a Subjective Expected Utility (SEU) representation of preferences over acts, involving a continuous utility function on X (unique up to positive affine transformations), and a unique probability measure on a Boolean algebra B of regular open subsets of S. With additional topological hypotheses, we obtain a unique Borel probability measure on S, along with an auxiliary apparatus called a liminal structure, which describes the agent’s informational constraints. We also obtain SEU representations involving subjective state spaces, such as the Stone-Čech compactification of S and the Stone space of B

Subjective expected utility with imperfect perception

In many decisions under uncertainty, there are constraints on both the available information and the feasible actions. The agent can only make certain observations of the state space, and she cannot make them with perfect accuracy —she has imperfect perception. Likewise, she can only perform acts that transform states continuously into outcomes, and perhaps satisfy other regularity conditions. To incorporate such constraints, we modify the Savage decision model by endowing the state space S and outcome space X with topological structures. We axiomatically characterize a Subjective Expected Utility (SEU) representation of conditional preferences, involving a continuous utility function on X (unique up to positive affine transformations), and a unique probability measure on a Boolean algebra B of regular open subsets of S. We also obtain SEU representations involving a Borel measure on the Stone space of B — a “subjective” state space encoding the agent’s imperfect perception

Dynamic consistency of expected utility under non-classical(quantum) uncertainty

Quantum cognition is a recent and rapidely growing field. In this paper we developan expected utility theory in a context of non-classical (quantum) uncertainty.We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework we formulate sufficient and necessary axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neuman-Luders postulate applied to beliefs. In our context, dynamic consistency is shown not to secure Savage's Sure Thing Principle (in its dynamic version). Finally, we discuss the interpretation and value of our results for rationality and behavioral economics

Subjective expected utility with topological constraints

In many decisions under uncertainty, there are technological constraints on the acts an agent can perform and on the events she can observe. To model this, we assume that the set S of possible states of the world and the set X of possible outcomes each have a topological structure. The only feasible acts are continuous functions from S to X, and the only observable events are regular open subsets of S. We axiomatically characterize Subjective Expected Utility (SEU) representations of conditional preferences over acts, involving a continuous utility function on X (unique up to positive affine transformations), and a unique Borel probability measure on S, along with an auxiliary apparatus called a "liminal structure", which describes the agent’s imperfect perception of events. We also give other SEU representations, which use residual probability charges or compactifications of the state space

Dynamically consistent preferences under imprecise probabilistic information

Riedel F, Tallon J-M, Vergopoulos V. Dynamically consistent preferences under imprecise probabilistic information. Center for Mathematical Economics Working Papers. Vol 573. Bielefeld: Center for Mathematical Economics; 2017.This paper extends decision theory under imprecise probabilistic information to dynamic settings. We explore the relationship between the given objective probabilistic information, an agent's subjective multiple priors, and updating. Dynamic consistency implies rectangular sets of priors at the subjective level. As the objective probabilistic information need not be consistent with rectangularity at the subjective level, agents might select priors outside the objective probabilistic information while respecting the support of the given set of priors. Under suitable additional axioms, the subjective set of priors belongs to the rectangular hull of the objective probabilistic information