Schedule - Parallel Session 4 - Measuring Risk Preferences

This paper presents results of a study which shed new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation concerns (possibly discontinuous) jumps in indifference curves at the triangle legs towards the triangle origin. Such jumps, however, do not appear at the triangle hypotenuse. This points out to discontinuity in the lottery valuation when the range of the lottery outcomes changes. This observation is confirmed by fitting six decision-making models: Expected Utility Theory, Prospective Reference Theory, Cumulative Prospect Theory, the TAX model, Salience Theory, and Decision Utility Theory. Those models, which correctly predict jumps at the triangle legs (CPT is not among them), offer the best fit of the data collected. Focusing attention to the range of lottery outcomes appears thus one of the most important psychological factors driving decisions under risk. Interestingly, the shape of the indifference curves and the model ranking changes when lotteries close to the triangle boundaries are excluded from considerations: the pattern reminds then the “fanning-out” hypothesis and CPT is the winner. The study has been made using a novel non-parametric method of estimating indifference curves, which is based on linear interpolation of certainty equivalent values between adjacent points representing the lotteries under consideration. This allows to plot indifference curves, certainty equivalent 3D surfaces and to estimate slopes of indifference curves in the triangle sub-areas. Moreover, the indifferences curves estimated non-parametrically can be graphically compared with those predicted by the models. This helps to understand why some models perform better or worse depending on the set of lotteries.

Experimental research shows that the preferences that people express in surveys and experiments are often characterised by a considerable degree of noise or imprecision. While preferences are treated as primitive in economics, imprecision is often ignored or simply modelled as an ad hoc white noise term that is appended to otherwise standard preferences. For preference imprecision to be recognised as a meaningful concept in economics, its credentials must be established by (a) being able to reliably measure it, and (b) showing that it is systematically related to choice behaviour.
Our paper addresses these issues in the context of decision-making under risk, a setting in which preference imprecision has often been observed as a tendency for many participants to reverse their preferences over pairs of lotteries when presented with them two or more times during the course of the same experiment. We seek to elicit straightforward measures of preference imprecision that can be easily linked to choice behaviour, regarded by many as the gold standard in preference elicitation.
We conduct an experiment in which we allow participants to express imprecision in their preferences by reporting that, while they prefer one lottery over another, they are not sure about their preference. In the first part of our experiment, we present participants with tables containing series of paired options in which one is kept constant and the other is made progressively better (by varying either a money amount or a probability), in order to identify a range of imprecision, that is, a range of money amounts or probabilities over which they are less than sure about whether they prefer the lottery that is kept constant. In the second part of our experiment, we build a comprehensive picture of each participant’s revealed (but potentially probabilistic) preferences over a circumscribed space of lotteries by asking them to make a large number of repeated choices between pairs of lotteries, presented in a random sequence determined independently for each participant.
By their nature, our measures of self-reported imprecision (MoI) cannot be made incentive-compatible, but rely on participants’ desire to provide informative responses. Our validation strategy consists in exploring the extent to which our MoI map into the participants’ choice behaviour. For each participant, we are able to identify the relationship between the ranges he/she reports in the first part of the experiment and the choices that she makes in the second. While the exact mapping between choice probabilities and the reported imprecision ranges may vary between participants, if they are sufficiently able to introspect about the noisiness of their preferences, we expect to find that wider ranges of imprecision correspond to cases in which choices are less predictable – i.e. choice probabilities are less extreme. Our preliminary results show that participants are prone to report that they are not sure about their preferences, but their ranges of imprecision do not correlate closely with the noise revealed by their choice probabilities.