Random expected utility and certainty equivalents: mimicry of probability weighting functions

Nathaniel T. Wilcox
2017 Journal of the Economic Science Association  
For simple prospects routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank dependent preferences. That is, a subject with random expected utility preferences can have expected certainty equivalents exactly like those predicted by rank dependent probability weighting functions of the inverse-s shape discussed by Quiggin (1982) and advocated by Tversky and Kahneman (1992), Prelec (1998)
more » ... 2), Prelec (1998) and other scholars. Certainty equivalents may not nonparametrically identify preferences: Their conditional expectation (and critically, their interpretation) depends on assumptions concerning the source of their variability. provided help or commentary, though none are responsible for remaining errors. Elicitation of certainty equivalents has become routine in laboratory measurement of preferences under risk and uncertainty (Tversky and Kahneman Bruhin, Fehr-Duda and Epper 2010; Vieider et al. 2015). While elicitation methods vary across such studies, formal empirical interpretations of elicited certainty equivalents are invariably the same. The subject is assumed to have a unique and fixed preference order, implying (under unchanged conditions of background wealth, risk and so forth) a unique and fixed certainty equivalent for each prospect. Elicited certainty equivalents are then interpreted as this unique and fixed certainty equivalent plus some error of banal origin with standard properties. Such added error, or something like it, is necessary: In repeated elicitations using exactly the same prospect, elicited certainty equivalents vary within subjects (Tversky and and other evidence also suggests inherent variability of elicited certainty equivalents (e.g. Butler and Loomes 2007). Luce (1997, pp. 81-82) argued that theory and empirical interpretation need to take a position on such response variability. Adding mean zero error to an otherwise deterministic model of certainty equivalents is clearly one option here, and I call this the standard model of an elicited certainty equivalent. Random preference models are a well-known alternative to standard models. These models assume that an individual subject's preference order is a random variable, and that each certainty equivalent elicited from that subject is fully determined by a single realization of that random variable. Random preference models are both old and contemporary, particularly in the realm of discrete choice (Becker, ). I examine implications of random preference models for elicited certainty equivalents and find a significant complication of their empirical interpretation. Random model expected utility preferences (or more simply random EU as Gul and Pesendorfer call it) imply expected certainty equivalents that can mimic those implied by standard model rank-Pennings, J. M. E. and A. Smidts, 2000, Assessing the construct validity of risk attitude. Management Science 46:1337-1348. Powell, M. J. D., 1992, A direct search optimization method that models the objective and constraint functions by linear interpolation.
doi:10.1007/s40881-017-0042-1 fatcat:nyzruxgzrfgbzf7hyowpypfimm