International Choice Modelling Conference, International Choice Modelling Conference 2015

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Are we standard or non-standard expected utility maximizers? Discrete mixture models of choice over food-safety policies with risky outcomes
Simone Cerroni, Sandra Notaro, Roberta Raffaelli

Last modified: 18 May 2015


During the last couple of decades, the investigation of choice-behaviour under conditions of risk has been increasingly investigated in the stated-preference (SP) literature. However, only few recent investigations have examined preferences over lotteries that involve non-financial outcomes (e.g., Hensher et al., 2011). This increasing interest in choice-behaviour related to non-financial lotteries is mainly due to a couple of reasons. The first is that most of everyday choices (not only financial) involve some degree of uncertainty. The second reason is that choice-behaviour under risk might be context dependent (e.g., Riddel 2012).

More interestingly, as a massive amount of empirical work has demonstrated the poor ability of Expected Utility Theory (EUT) to explain observed behaviour, few SP studies have explored to what extent the standard and non-standard theories of choice under risk can explain choices related to lotteries that involve non-financial outcomes (e.g., Hensher and Li, 2012). The common approach that has been used to compare the ability of alternative theories of choice under risk to explain choices consists in estimating alternative empirical models, each relying on an alternative theory. Once competing models have been estimated, the best one is identified by comparing estimated coefficients and data fit criteria. This approach clearly relies on the assumption that the data is only generated by one identifiable latent decision-making process at the time (Harrison and Rutström 2009).

In this paper, we investigate to what extent standard and non-standard theories of choice under risk explain choices among lotteries that involve non-financial outcomes using another approach based on the estimation of discrete mixture models. Using data collected via a hypothetical choice experiment field survey, we estimate two discrete mixture models that allow different subjects to make choices according to different theories of choices under risk. Here, we focus on EUT, Rank-Dependent Expected Utility Theory (RDEUT) and Regret Theory (RT). These two models are used to compare RDEUT-based and RT-based models with a standard EUT-based model respectively, and assess the proportion of choices that can be explained by standard and non-standard expected utility theories. Note that our RT-based model is an extension of the standard Random Regret Minimization model developed by Chorus for riskless outcomes (2010). The extension consists in applying the RRM model in a probabilistic framework to reconcile the Chorus’ intuition to the original RT developed by Loomes and Sudgen in 1982. To our knowledge, this is the first attempt to use a mixture model to investigate choices over lotteries with non-financial outcomes (see Harrison and Rutström 2009 and Conte et al., 2011 for financial lotteries’ examples).

In our application, the non-financial risky outcome under study is the number of apples that will contain pesticide residues in the Province of Trento (Italy) in 2030. More specifically, our CE survey aims to elicit people’s preferences for the R&D programs that will reduce the number of contaminated apples in 2030. Each subject is presented with 12 choice tasks, each containing two alternative R&D programs plus an opt-out alternative that describes a scenario in which no R&D program is implemented. Each alternative is a lottery with two states of world, namely i and j, so that each subject face a probability pi of experiencing a given number of contaminated apples ni and a probability pj of experiencing a given number of contaminated apples nj. While there is an annual tax to pay associated with R&D programs, there is no tax to pay associated with the no R&D program alternative.

Results from our mixture models’ estimations show the majority of our sample (66%) makes choices that do not depart from EUT, while the remaining proportion of subjects behave accordingly to RDEUT (34%). In addition, subjects who behave accordingly to RDEUT have a probability weighting function that has an inverse-S shape strikingly similar to that found in many controlled laboratory experiment (e.g., Harrison and Rutström, 2008). This implies that subjects overweight small probability losses (i.e., probabilities smaller than 0.37), while they underweight large probability losses (i.e., probabilities greater than 0.37). An intuitive interpretation of this result is that our subjects are moderately risk averse for small probability losses and moderately risk seeking for large probability losses. An alternative intriguing interpretation is that our subjects are moderately pessimistic with respect to small probability losses, while they are moderately optimistic with respect to large probability losses (Wakker 2010).

Estimations of our mixture models also suggest that few subjects make choices according to our RT-extended model (11%) in our empirical application. Again, this indicates that departures form EUT should be taken into account in modelling choice behaviour, but these are not necessarily the norm.





Chorus, C.G. 2010. “A New Model of Random Regret Minimization.” European Journal of Transport and Infrastructure Research 10(2): 181-196.


Conte, A., J.D. Hey, and P.G. Moffat. 2011. “Mixture models of choice under risk.” Journal of Econometrics 162: 79-88.


Harrison, G. W. and E. E. Rutström. 2008. “Risk aversion in the laboratory”. In J. C. Cox and G. W. Harrison, eds. Research in experimental economics: Vol. 12. Risk aversion in experiments. Bingley: Emerald.


Harrison, G.W., and E.E. Rutström. 2009. “Expected utility theory and prospect theory: one wedding and a decent funeral.” Journal of Experimental Economics 12(2): 133-158.


Hensher, D.A., W.H. Greene, and Z. Li. 2011. “Embedding risk attitudes and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings.” Transportation Research Part B 45: 954-972.


Hensher, D.A., and Z. Li. 2012. “Valuing travel time variability within a rank-dependent utility framework and an investigation of unobserved taste heterogeneity.” Journal of Transport Economics and Policy 46(2): 293-312.


Loomes, G., and R. Sudgen. 1982. “Regret Theory: An Alternative Theory of Rational Choice under Uncertainty.” The Economic Journal 92(368): 805-824.


Riddel, M. 2012. “Comparing risk preferences over financial and environmental lotteries.” Journal of Risk and Uncertainty 45(2): 135-157.


Wakker, P. 2010. Prospect theory for risk and ambiguity. Cambridge, UK: University Press








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