Yang, Jingni & Peter P. Wakker (2017) “Generalizing Many Theorems on Concave/Convex Utility or Weighting Functions,” working paper.

ABSTRACT. This paper shows that convexity of preference has stronger implications for weighted utility models than had been known hitherto, both for utility and for weighting functions. Our main theorem derives concave utility from convexity of preference on the two-dimensional comonotonic cone, without presupposing continuity. Using this seemingly marginal result, we then obtain the most appealing and general axiomatizations of concave/convex utilities and decision weights for many decision models. Included are: risk aversion in expected utility, optimism/pessimism in rank-dependent utility and prospect theory, uncertainty aversion in Choquet expected utility, ambiguity aversion in the smooth model, and inequality aversion in utilitarianism. We provide some surprising relations between well-known conditions, e.g.: in Yaari’s dual theory, convexity/concavity in (“horizontal”) outcome mixing are not only dual, but also logically equivalent, to concavity/convexity in (“vertical”) probability mixing.

Bleichrodt, Han, Jason N. Doctor, Yu Gao, Chen Li, Daniella Meeker, & Peter P. Wakker (2017) “Resolving Rabin’s Paradox,” working paper.

ABSTRACT. Controversies and confusions have arisen as to whether Rabin’s classical paradox truly violates expected utility and, more generally, reference dependence, partly due to different terminologies in different fields. By providing the proper theoretical model, we resolve the confusions and make it possible to identify the causes of this long-standing paradox. Further, through use of proper experimental stimuli, we can test the empirical relevance of these causes. Based on direct and indirect (excluding all other causes) evidence, we identify violations of reference independence as the true culprit. Thus, Rabin’s paradox provides a positive message, underscoring the importance of reference dependence.

Aurélien Baillon, Zhenxing Huang, Asli Selim, & Peter P. Wakker (2016) “Measuring Ambiguity Attitudes for All (Natural) Events,” working paper. Online Appendix.

ABSTRACT. Measurements of ambiguity attitudes have so far focused on artificial events, where subjective beliefs can be derived from symmetry assumptions. For natural events such assumptions usually are not available, creating a difficulty in calibrating subjective beliefs and, hence, in measuring ambiguity attitudes. This paper introduces a simple control for subjective beliefs even when they are unknown. We thus allow for a tractable and completely revealed-preference based 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 indexes are valid under many ambiguity theories. They do not require expected utility for risk, which is desirable for empirical purposes. Furthermore, they are easy to elicit in practice. An experiment on ambiguity under time pressure shows the tractability of our method. It gives plausible results, supporting the validity of our indexes.

Johnson, Cathleen, Aurélien Baillon, Han Bleichrodt, Zhihua Li, Dennie van Dolder, Peter P. Wakker (2014) “Prince: An Improved Method For Measuring Incentivized Preferences,” working paper.

ABSTRACT. This paper introduces the prior incentive system (Prince) for measuring preferences. Prince clarifies consequences of decisions and incentive compatibility of experimental choice questions. It combines the efficiency and precision of matching with the improved clarity and validity of choice questions. It helps distinguish between (a) genuine deviations from classical economic theories (such as the endowment effect) and (b) preference anomalies due to fallible measurements (such as preference reversals). Prince avoids (a) opaqueness in Becker-DeGroot-Marschak; (b) violations of isolation in the random incentive system; and (c) strategic behavior in adaptive experiments. Using Prince we shed new light on willingness to accept, subjective probabilities and utilities, and ambiguity attitudes.

Trautmann, Stefan & Peter P. Wakker (2015) “Making the Anscombe-Aumann Approach to Ambiguity Suitable for Descriptive Applications,” working paper. Online Appendix.

ABSTRACT. The Anscombe-Aumann (AA) model, originally introduced to give a normative basis to expected utility, is nowadays mostly used for another purpose: to analyze deviations from expected utility due to ambiguity (unknown probabilities). The AA model makes two ancillary assumptions that do not refer to ambiguity: expected utility for risk and backward induction. These assumptions, even if normatively appropriate, fail descriptively. We relax them while maintaining AA's convenient mixture operation, and thus make it possible to test and apply AA based ambiguity theories descriptively. We find three common assumptions violated: reference independence, universal ambiguity aversion, and weak certainty independence. We introduce and axiomatize a reference dependent generalization of Schmeidler's CEU theory that accommodates the violations found. That is, we extend the AA model to prospect theory.

**Last updated:** 18 November, 2017

**(back to Peter Wakker's homepage)
**