Accommodating stake effects under prospect theory

Abstract

One of the stylized facts underlying prospect theory is a fourfold pattern of risk preferences. People have been shown to be risk seeking for small probability gains and large probability losses, while being risk averse for large probability gains and small probability losses. Another fourfold pattern of risk preferences over outcomes, postulated by Harry Markowitz in 1952, has received much less attention and is currently not integrated into prospect theory. In two experiments, we show that risk preferences may change over outcomes. While we find people to be risk seeking for small outcomes, this turns to risk neutrality and later risk aversion as stakes increase. We then show how a one-parameter logarithmic utility function fits such stake effects significantly better under prospect theory than the power or exponential functions mostly used when fitting prospect theory models. We further investigate the extent to which the use of ill-suited functional forms to represent utility may result in violations of prospect theory, and whether such violations disappear when using logarithmic utility.

Your money and your life: Risk attitudes over gains and losses

“…This pattern becomes more evident as outcome size declines, and can be attributed to more respondents demonstrating SS patterns at the expense of AS patterns. In other words, with smaller outcomes more respondents were willing to throw caution to the wind in the gains domain, which, in and of itself, is a phenomenon that was predicted by Markowitz and was also observed by Bouchouicha and Vieider (2017). 6 Although Markowitz overlooked the possible effect of subjective probability on observations of reflection, which prevented him from seeing the full descriptive picture of risk-related decision 6 Bouchouicha and Vieider (2017) similarly did not observe the Markowitz prediction of risk seeking increasing with the magnitude of losses.…”

“…Moreover, in a recent article, Bouchouicha and Vieider (2017) reported results from an incentivised study over gains only and from a non-incentivised study over gains and losses. In order to elicit the certainty equivalent of each money gamble in their studies they presented their respondents with a series of pairwise choices between the gamble in question and a number of sure amounts.…”

“…Since the Markowitz model has also attracted some attention in the recent literature (e.g. Bouchouicha and Vieider 2017;Levy and Levy 2002;Scholten and Read 2014), its risk attitude predictions for small to sizable but not huge outcomes are also presented in the table, and will be referred to below.…”

“…13 That said, if the status quo is an unbearable proposition to the patient, then the desire to undertake a one-shot treatment may be rational in a broad sense of the term irrespective of how many orders of magnitude worse than the status quo is the outcome of treatment failure (assuming that it is possible to have outcomes that are orders of magnitude worse than 'unbearable'), given that treatment offers at least some prospect of escaping the already unbearable status quo. 14 Remember, however, that Bouchouicha and Vieider (2017) used a sequence of pairwise choices to elicit certainty equivalencies, and found evidence in support of prospect theory's fourfold reflection effect.…”

All over the map: A worldwide comparison of risk preferences

“…The former expresses an attitude towards risk (increasing uncertainty hurts), whereas the latter expresses an attitude towards wealth (the loss of a sheep hurts more when an agent is poor than when an agent is rich)” (p. 95). While utility curvature is clearly important when stakes are large, allowing for nonlinear utility generally only takes up some of the risk preferences otherwise captured in probability weighting over the relatively modest stake ranges we use (see Bouchouicha and Vieider (), for specific evidence on stake variation under PT). This simplification further provides a good compromise between descriptive fit and tractability.…”