Schedule - Parallel Session 3 - Ambiguity: Theory and Applications 1

IMC Auditorium - 15:40 - 17:10

An Axiomatisation of Discrete Possibilistic Choquet Integrals

Agnès Rico; Didier Dubois


Necessity (resp. possibility) measures are special cases of Shafer belief functions (resp. plausibility measures) that are infimum-preserving (resp. supremum preserving). They are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit of being very simple to define and compute. It has been used already in signal processing, and in multiple-stage decision-making. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decision-maker preferences only reflect the plausibility ordering between states of nature. The class of functions with respect to which Choquet integral is additive is enlarged, as any act is provably indifferent to some other act that is comonotonic (in the pessimist case) or anti-comonotonic (in the optimistic case) with the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an averaged maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The pessimistic attitude of the decision-maker expresses the idea that the consequence of a decision in a state is never more attractive than the least attractive consequences over states that are more plausible than this state. An axiomatisation of these criteria for decision under uncertainty is also proposed in the setting of preference relations among acts. Our work differs from the one of Rebille, which proposes a possibilistic counterpart, to the comparison of necessity measures, of Von Neumann-Morgenstern approach. Our results can be compared with the axiomatic approach to max-min ordinal possibilistic criteria proposed in the early 2000’s.

Agnès Rico

Directeur de Recherche au CNRS, Claude Bernard Lyon 1

Measuring Ambiguity Attitudes for All (Natural) Events

Peter Wakker


Ambiguity attitudes have so far been measured only for artificial events, where subjective beliefs can be directly derived from symmetry arguments. For natural events such symmetry arguments are usually not available, creating a difficulty in calibrating subjective beliefs for them and, hence, for measuring ambiguity attitudes with respect to them. This paper introduces a control for subjective beliefs even when they are unknown, allowing for the measurement of ambiguity attitudes for all events, including natural ones. We introduce indexes of ambiguity aversion and ambiguity perception (or understanding) that generalize and unify many existing indexes. Our indices are theoretically founded, and easy to elicit in practice. In an experiment on ambiguity under time pressure, we obtain plausible results: time pressure affects people’s perception and understanding of ambiguity but not their aversion. Our indexes are valid under many ambiguity theories and do not require expected utility for risk, which is desirable for empirical purposes.

Peter Wakker

Professor, Erasmus University Rotterdam

From Anomalies to Forecasts

Ido Erev; Eyal Ert; Ori Plonsky; Doron Cohen; Oded Cohen


Experimental studies of choice behavior document distinct, and sometimes contradicting, deviations from maximization in different settings and experimental paradigms. Specifically, different behavioral phenomena emerge in decisions under risk and decisions under ambiguity, in decisions from description and decisions from experience, and in choice between binary gambles and choice between multi-outcome gambles. Most previous efforts to develop descriptive models of choice behavior address the distinct results by assuming different processes and proposing different models (or parameters) capturing the different choice anomalies. Implicit in these efforts is the assumption that the task of developing descriptive models is similar to the task of solving a puzzle: It is wise to start with a focus on the easy and interesting problems (areas); and the progress (added parts) will eventually clarify the more difficult areas, and the relationship between the different areas. The current paper evaluates an alternative approach: We consider the possibility that the development of descriptive models is more similar to the game “Scratch and Guess.” The optimal strategy in this game is to distribute the data collection efforts over a wide space to facilitate evaluation of the big picture. That is, we try to develop a general model capturing the coexistence and relative importance of the contradicting tendencies shown to emerge in different settings. Three steps are taken to reduce the risk of overfitting the data. First, we replicate 14 classical anomalies in one experimental paradigm. Next, we studied 60 problems randomly selected from a space that includes all problems examined in the replication study. Finally, to reduce the danger of an arbitrary selection of feasible models, an open choice prediction competition was organized. The organizers (first three co-authors) presented their favorite model and challenged other researchers to develop better models. Models were evaluated based on their predictions of 60 new problems. The results suggest that the classical “pre-feedback” phenomena are replicable, but that feedback eliminates most and instigates choice of the prospect minimizing probability of regret. The models that best capture the results assume: (a) high sensitivity to the best estimates of the expected values, (b) the use of several feedback-dependent heuristics, and (c) reliance on small samples.

Preference Incompleteness and the Gains from Trade

Tigran Melkonyan; Robert Chambers


Behavioral inertia is familiar in everyday experience, in economic laboratory experiments, in economic field experiments, and in market settings. Even children understand the proverb: “When in doubt, do nothing!”. A variety of explanations have been advanced for such behavior. A prominent economic explanation is incompleteness of preference structures, especially in the presence of ambiguity (Aumann, 1962; Bewley, 2002). This paper shows that whether incomplete preferences rationalize behavioral inertia depends crucially upon the choice set supporting the initial status quo. We illustrate in trade theoretic terms. If preferences are complete, two countries with the same tastes, technologies, and resource endowments would not be expected to trade. This reflects a lack of mutually beneficial opportunities to trade. But our analysis shows that when preferences are incomplete and the technology is suitably convex, two countries with the same tastes, technologies, and resource endowments face potential gains from intercountry trade for generic status quo allocations. Therefore, trade can be expected to emerge. Although other studies have analyzed trade with non-expected utility preferences and production technologies (for example, Bewley 2002; Mandler 2013, Chambers 2014), to our knowledge none have characterized this particular trade-creating effect. The intuitive argument is that for any potential status-quo allocation, the kinkiness of the decisionmaker’s indifference contour ensures that a continuum of marginal rates of substitution is consistent with equilibrium for that allocation. That continuum of marginal rates of substitution is consistent with equilibrium for a matching continuum of marginal rates of transformation. If the choice set supporting the status-quo is strictly convex, each marginal rate of transformation maps into an unique efficient point implying that a continuum of status-quo equilibria potentially exists. Even though these potential equilibria may be highly disparate, none is strictly preferred to the others. Hence, starting from any one of these equilibria, if the decisionmaker were to rely on autarkic adjustment alone, inertia would result. Now suppose that the decisionmaker is allowed not only to move between efficient points but also to trade with another identical individual whose status-quo allocation is one of these alternative efficient points. The differences in the underlying marginal rates of transformation ensure that potential benefits exist from agreeing to trade. Preference incompleteness, as compared with preference completeness, creates the heterogeneity necessary in autarkic allocations to ensure the potential to gain from trade. Thus, the possibility of substitution in production coupled with incompleteness of preferences can result in more trade and not less.

Tigran Melkonyan

Associate Professor, University of Warwick