Many popular internet platforms use so-called collaborative filtering systems to give personalized recommendations to their users, based on other users who provided similar ratings for some items. We propose a novel approach to such recommendation systems by viewing a recommendation as a way to extend an agent's expressed preferences, which are typically incomplete, through some aggregate of other agents' expressed preferences. These extension and aggregation requirements are expressed by an Acceptance and a Pareto principle, respectively. We characterize the recommendation systems satisfying these two principles and contrast them with collaborative filtering systems, which typically violate the Pareto principle.

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We propose and operationalize normative principles to guide social decisions when individuals potentially have imprecise and heterogeneous beliefs, in addition to conflicting tastes or interests. To do so, we adapt the standard Pareto principle to those preference comparisons that are robust to belief imprecision and characterize social preferences that respect this robust principle. We also characterize a suitable restriction of this principle. The former principle provides stronger guidance when it can be satisfied; when it cannot, the latter always provides minimal guidance.

We provide a generalization of Harsanyi's (1955) aggregation theorem to the case of incomplete preferences at the individual and social level. Individuals and society have possibly incomplete expected utility preferences that are represented by sets of expected utility functions. Under Pareto indifference, social preferences are represented through a set of aggregation rules that are utilitarian in a generalized sense. Strengthening Pareto indifference to Pareto preference provides a refinement of the representation. (JEL D01, D11, D71)

We provide possibility results on the aggregation of beliefs and tastes for Monotone, Bernoullian and Archimedian preferences of Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci, and Siniscalchi (2011). We propose a new axiom, Unambiguous Pareto Dominance, which requires that if the unambiguous part of individuals’ preferences over a pair of acts agree, then society should follow them. We characterize the resulting social preferences and show that it is enough that individuals share a prior to allow non dictatorial aggregation. A further weakening of this axiom on common-taste acts, where cardinal preferences are identical, is also characterized. It gives rise to a set of relevant priors at the social level that can be any subset of the convex hull of the individuals’ sets of relevant priors. We then apply these general results to the Maxmin Expected Utility model, the Choquet Expected Utility model and the Smooth Ambiguity model. We end with a characterization of the aggregation of ambiguity attitudes.

We analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals and society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. This class turns out to be considerably broader for indeterminate than for determinate utilities, where it basically reduces to utilitarianism. In particular, aggregation rules may differ by the relationship between individual and social indeterminacy. We characterize several subclasses of neutral aggregation rules and show that utilitarian rules are those that yield the least indeterminate social utilities, although they still fail to systematically yield a determinate social utility.

We present an axiomatic model of preferences over menus that is motivated by three assumptions. First, the decision maker is uncertain ex ante (i.e., at the time of choosing a menu) about her ex post (i.e., at the time of choosing an option within her chosen menu) preferences over options, and she anticipates that this subjective uncertainty will not resolve before the ex post stage. Second, she is averse to ex post indecisiveness (i.e., to having to choose between options that she cannot rank with certainty). Third, when evaluating a menu she discards options that are dominated (i.e., inferior to another option whatever her ex post preferences may be) and restricts attention to the undominated ones. Under these assumptions, the decision maker has a preference for commitment in the sense of preferring menus with fewer undominated alternatives. We derive a representation in which the decision maker’s uncertainty about her ex post preferences is captured by means of a subjective state space, which in turn determines which options are undominated in a given menu, and in which the decision maker fears, whenever indecisive, to choose an option that will turn out to be the worst (undominated) one according to the realization of her ex post preferences.

We analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals ans society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. This class turns out to be considerably broader for indeterminate than for determinate utilities, where it basically reduces to utilitarianism. In particular, aggregation rules may differ by the relationship between individual and social indeterminacy. We characterize several subclasses of neutral aggregation rules and show that utilitarian rules are those that yield the least indeterminate social utilities, although they still fail to systematically yield a determinate social utility.

It is very rare to find in a single person both the qualities of a remarkable scientific mind and of a wonderful human being. With this tribute to Jean-Yves Jaffray, we hope to convince the reader of his outstanding creativity and vision, of the coherence of his work, and of its relevance for some topics in decision theory that are currently under lively debate. As a scientist, Jean-Yves Jaffray can be characterized by one main insight and one main concern. His main insight is that a sound decision theory must explicitly use all the information available to the decision maker. This information about events must further be treated in a strictly objective manner. In the models he proposed as a result, objective information can be disentangled from subjective attitudes with respect to this information. For that purpose, before asking how to represent preferences, one must wonder how to treat and represent the given information. Jean-Yves’ main concern in designing his models is that they must be tractable, implementable and testable. This leads him to emphasize the simplicity of the models he puts forward, including the way the arrival of new information is modeled, and to develop experiments to test them. This adherence to objectivity together with his concern for implementable models fits well with Jean-Yves’ applied work in statistics and computer science that we will not review here. After some words on his early contributions, we will discuss the way he addressed different questions linked to Decision Theory : How to describe information (or lack of information) on events? How to model decisions in this framework? How to evaluate decisions? How to update in the presence of new

Decision makers sometimes have to choose between alternative options about which they have no preference: either they judge the options equally valuable (indifference) or they have no judgment about their relative value (noncomparability). Choosing randomly is generally considered a natural way to deal with such situations. This paper shows, however, that systematic randomization between noncomparable options may lead to a chain of decisions resulting in monetary losses (a money pump). Furthermore, these losses can be avoided by deliberately selecting one of the noncomparable options instead of randomizing. Thus, randomization among noncomparable options is costly relative to deliberate selection. On the other hand, randomization among indifferent options is costless relative to deliberate selection.

Tribute to Jean-Yves Jaffray by the French Group of Decision Theory.

It is shown that preferences can be constructed from observed choice behavior in a way that is robust to indifferent selection (i.e., the agent is indifferent between two alternatives but, nevertheless, is only observed selecting one of them). More precisely, a suggestion by Savage [Savage, L.J., 1954. The foundations of statistics. John Wiley and Sons] to reveal indifferent selection by considering small monetary perturbations of alternatives is formalized and generalized to a purely topological framework: preferences over an arbitrary topological space can be uniquely derived from observed behavior under the assumptions that they are continuous and nonsatiated and that a strictly preferred alternative is always chosen, and indifferent selection is then characterized by discontinuity in choice behavior. Two particular cases are then analyzed: monotonic preferences over a partially ordered set, and preferences representable by a continuous pseudo-utility function.

We propose an experimental design allowing a behavioral test of the axiom of completeness of individual preferences. The central feature of our design consists in enabling subjects to postpone commitment at a small cost. Our main result is that preferences are significantly incomplete. We use lotteries as choice alternatives and we find that risk aversion is globally robust to preference incompleteness.

Completeness, the most commonly assumed axiom in preference theory, has not received much attention from the experimental literature. Indeed, incomplete preferences model a cognitive phenomenon (an agent's inability to compare alternatives), and therefore cannot be directly revealed through choice behavior. Implementing a solution to this methodological issue recently proposed by Danan [A behavioral model of individual welfare, mimeo EUREQua University Paris 1, 2003], we build an experimental protocol involving choices among menus of lotteries, and reveal cognitive preferences' incompleteness by means of the concept of preference for flexibility. Our experimental protocol is designed to assess the descriptive validity of the completeness axiom, as well as to relate its possible violations to lotteries' riskiness. Two-thirds of the subjects whose choices reveal preferences in accordance with the underlying theory exhibit a strictly positive measure of incompleteness. The observed average measure of incompleteness equals approximately 17 percent and it is significantly greater than 10 percent. We do not find a significant relationship between a lottery's riskiness and its cognitive comparability with certain payoffs.