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Despite the increasing importance of multiple priors in various domains of economics and the significant theoretical advances concerning them, choice-based incentive-compatible multiple-prior elicitation largely remains an open problem. This paper develops a solution, comprising a preference-based identification of a subject’s probability interval for an event, and two procedures for eliciting it. The method does not rely on specific assumptions about subjects’ ambiguity attitudes or probabilistic sophistication. To demonstrate its feasibility, we implement it in two incentivized experiments to elicit the multiple-prior equivalent of subjects’ cumulative distribution functions over continuous-valued sources of uncertainty. We find a predominance of non-degenerate probability intervals among subjects for all explored sources, with intervals being wider for less familiar sources. Finally, we use our method to undertake the first elicitation of the mixture coefficient in the Hurwicz α-maxmin EU model that fully controls for beliefs.

International audience; ConspectusThe chemical study of materials from natural history and cultural heritage, which provide information for art history, archeology, or paleontology, presents a series of specific challenges. The complexity of these ancient and historical materials, which are chemically heterogeneous, the product of alteration processes, and inherently not reproducible, is a major obstacle to a thorough understanding of their making and long-term behavior (e.g., fossilization). These challenges required the development of methodologies and instruments coupling imaging and data processing approaches that are optimized for the specific properties of the materials. This Account discusses how these characteristics not only constrain their study but also open up specific innovative avenues for providing key historical information. Synchrotron methods have extensively been used since the late 1990s to study heritage objects, in particular for their potential to provide speciation information from excitation spectroscopies and to image complex heritage objects and samples in two and three dimensions at high resolution. We examine in practice how the identification of key intrinsic chemical specificities has offered fertile ground for the development of novel synchrotron approaches allowing a better stochastic description of the properties of ancient and historical materials. These developments encompass three main aspects: (1) The multiscale heterogeneity of these materials can provide an essential source of information in the development of probes targeting their multiple scales of homogeneity. (2) Chemical alteration can be described in many ways, e.g., by segmenting datasets in a semiquantitative way to jointly inform morphological and chemical transformation pathways. (3) The intrinsic individuality of chemical signatures in artifacts triggers the development of specific strategies, such as those focusing on weak signal detection. We propose a rereading of the advent of these new methodologies for analysis and characterization and examine how they have led to innovative strategies combining materials science, instrument development, history, and data science. In particular, we show that spectral imaging and the search for correlations in image datasets have provided a powerful way to address what archeologists have called the uncertainty and ambiguity of the material record. This approach has implications beyond synchrotron techniques and extends in particular to a series of rapidly developing approaches that couple spectral and spatial information, as in hyperspectral imaging and spatially resolved mass spectrometry. The preeminence of correlations holds promise for the future development of machine learning methods for processing data on historical objects. Beyond heritage, these developments are an original source of inspiration for the study of materials in many related fields, such as environmental, geochemical, or life sciences, which deal with systems whose alteration and heterogeneity cannot be neglected.

This paper develops a belief update rule under ambiguity, motivated by the maxim: in the face of new information, retain those conditional beliefs in which you are more confident, and relinquish only those in which you have less confidence. We provide a preference-based axiomatisation, drawing on the account of confidence in beliefs developed in Hill (2013) . The proposed rule constitutes a general framework of which several existing rules for multiple priors (Full Bayesian, Maximum Likelihood) are special cases, but avoids the problems that these rules have with updating on complete ignorance. Moreover, it can handle surprising and null events, such as crises or reasoning in games, recovering traditional approaches, such as conditional probability systems, as special cases.

An ambiguous statistical experiment is a set of joint probability distributions over states and signals. This note compares ambiguous experiments from the point of view of an ambiguity averse decision maker and extends the Blackwell (1951, 1953) ordering to this setting.

It is commonly argued that dynamic consistency, consequentialism and non-expected utility are incompatible. The first aim of this paper is to rebut such arguments, by targeting the implicit assumption that the relevant contingencies correspond to objective resolutions of uncertainty (that is, events in a state space). These are not necessarily the same as the contingencies that the decision maker envisages, and we argue that any reasonable notion of dynamic consistency involves the latter, rather than the former, sort of contingency. We formulate such a version of dynamic consistency and show it to be compatible with consequentialism and non-expected utility. We then analyze the economic consequences of this new perspective. On the one hand, it provides a principled justification for restrictions on non-expected utility models (such as that proposed by Epstein and Schneider (2003)) in applications to dynamic choice problems. On the other hand, it provides a new analysis of the issue of attitude to information; contra standard arguments, the value of information under non-expected utility is non-negative as long as the information offered does not compromise information that the decision maker had otherwise expected to receive. Finally, we give a representation theorem for the contingencies the decision maker envisages, in the case where he uses the maxmin expected utility rule.

Entrepreneurship studies have attributed to over-confidence decisions to start a new venture. Many decision situations, through which over-confidence is measured, entail some degrees of uncertainty, (e.g., related to own skill or to competition). The aspect of uncertainty is largely neglected in over-confidence studies or entrepreneurial research. Both uncertainty and over-confidence influence individuals’ likelihood perceptions. Nevertheless, these two aspects are seldom jointly investigated, and the little evidence provides inconclusive results. In this study, we experimentally investigate how uncertainty, as a property of the situation, and over-confidence, as a characteristic of decision makers’ beliefs, influence choice behavior. Our findings with Executive MBA participants show that over-confident decision makers choose less uncertain options for low likelihood outcomes and more uncertain options for high likelihood outcomes, contrary to neutral confidence decision makers, whose choices are in line with standard Prospect Theory predictions.