Yang, Jingni & Peter P. Wakker (2018) “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 (2018) “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. The specific causes of expected utility’s unacceptable conclusions under Rabin’s paradox are also still unclear. We present a theoretical model that resolves the confusions and makes it possible to identify the causes of this long-standing paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and is caused by reference-dependence. Rabin already showed that utility cannot fully explain his paradox. We reach a stronger conclusion, that utility does not contribute anything at all to the explanation—and neither does probability weighting. Rabin’s paradox thus underscores the importance of reference dependence and loss aversion.

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.

**Last updated:** 26 July, 2018

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