This paper proposes a two-step method to successively elicit utility functions and decision weights under rank-dependent expected utility theory and its "more descriptive" version: cumulative prospect theory. The novelty of the method is that it is parameter-free, and thus elicits the whole individual preference functional without imposing any prior restriction. This method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains. Concave utility functions are obtained for gains and convex utility functions for losses. The elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations. The data also show that the probability weighting function for losses is more "elevated" than for gains.decision making, expected utility, rank-dependent expected utility, cumulative prospect theory, probability weighting function

International audienceA growing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion

International audienceWe often deal with uncertain events for which no probabilities are known. Several normative models have been proposed. Descriptive studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically. The theoretical key is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak

This paper provides an efficient method to measure utility under prospect theory, the most important descriptive theory of decision under uncertainty today. Our method is based on the elicitation of certainty equivalents for two-outcome prospects, a common way to measure utility. We applied our method in an experiment and found that most subjects were risk averse for gains and risk seeking for losses but had concave utility both for gains and for losses. This finding illustrates empirically that risk seeking and concave utility can coincide under prospect theory, a result that was derived theoretically by Chateauneuf and Cohen (1994). Utility was steeper for losses than for gains, which is consistent with loss aversion.Utility did not depend on the probability used in the elicitation, which offers support for prospect theory.

This paper reports the results of an experimental parameter-free elicitation and decomposition of decision weights under uncertainty. Assuming cumulative prospect theory, utility functions were elicited for gains and losses at an individual level using the tradeoff method. Subsequently, decision weights were elicited through certainty equivalents of uncertain two-outcome prospects. Furthermore, decision weights were decomposed using observable choice instead of invoking other empirical primitives, as in previous experimental studies. The choice-based elicitation of decision weights allows for a quantitative study of their characteristics, and also allows, among other things, for the examination of the sign-dependence hypothesis for observed choice under uncertainty. Our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice-based subjective probabilities. We also find evidence for sign dependence of decision weights.decision under uncertainty, Choquet expected utility, cumulative prospect theory, decision weights, choice-based probabilities, probability weighting

In an experiment, choice-based (revealed-preference) utility of money is derived from choices under risk, and choiceless (non-revealed-preference) utility from introspective strength-of-preference judgments. The well-known inconsistencies of risky utility under expected utility are resolved under prospect theory, yielding one consistent cardinal utility index for risky choice. Remarkably, however, this cardinal index also agrees well with the choiceless utilities, suggesting a relation between a choice-based and a choiceless concept. Such a relation implies that introspective judgments can provide useful data for economics, and can reinforce the revealed-preference paradigm. This finding sheds new light on the classical debate on ordinal versus cardinal utility. r

This paper uses "revealed probability trade-offs" to provide a natural foundation for probability weighting in the famous von Neumann and Morgenstern axiomatic set-up for expected utility. In particular, it shows that a rank-dependent preference functional is obtained in this set-up when the independence axiom is weakened to stochastic dominance and a probability trade-off consistency condition. In contrast with the existing axiomatizations of rank-dependent utility, the resulting axioms allow for complete flexibility regarding the outcome space. Consequently, a parameter-free test/elicitation of rank-dependent utility becomes possible. The probability-oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk. It is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade-off conditions.

International audienceThis paper reports on the results of an experimental elicitation at the individual level of all prospect theory components (i.e., utility, loss aversion, and weighting functions) in two decision contexts: situations where alternatives are described as probability distributions and situations where the decision maker must experience unknown probability distributions through sampling before choice. For description-based decisions, our results are fully consistent with prospect theory's empirical findings under risk. Furthermore, no significant differences are detected across contexts as regards utility and loss aversion. Whereas decision weights exhibit similar qualitative properties across contexts typically found under prospect theory, our data suggest that, for gains at least, the subjective treatment of uncertainty in experience-based and description-based decisions is significantly different. More specifically, we observe a less pronounced overweighting of small probabilities and a more pronounced underweighting of moderate and high probabilities for experience-based decisions. On the contrary, for losses, no significant differences were observed in the evaluation of prospects across contexts