Risk and rationality: The effects of mood and decision rules on probability weighting

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Abstract

Empirical research has shown that people tend to overweight small probabilities and underweight large probabilities when valuing risky prospects, but little is known about factors influencing the shape of the probability weighting curve. Based on a laboratory experiment with monetary incentives, we demonstrate that pre-existing good mood is significantly associated with women’s probability weights: Women in a better than normal mood tend to weight probabilities relatively more optimistically. Many men, however, seem to be immunized against effects of incidental mood by applying a mechanical decision criterion such as maximization of expected value.

Research highlights

► We investigate experimentally mood effects on risk taking behavior. ► We find strong gender differences in mood-sensitivity of risk aversion. ► Women in good mood are more optimistic than women in a normal mood state. ► Men are more likely to calculate expected values when assessing risky prospects. ► Applying such a decision rule makes men less susceptible to mood states.

Introduction

In the past decades, abundant experimental evidence has challenged the canonical economic model of decision under risk, expected utility theory. A large number of findings suggest that people systematically violate the axioms of expected utility theory (for a review see Starmer, 2000). In particular, people’s choices often exhibit a fourfold pattern: They are risk averse for high-probability gains and low-probability losses, and risk seeking for low-probability gains and high-probability losses. This phenomenon led Kahneman and Tversky, 1979, Tversky and Kahneman, 1992 to incorporate an inverse S-shaped probability weighting function as a core component in their prospect theory.

But why would people weight objective probabilities? Kahneman and Tversky justify the shape of the probability weighting function by the psychological principle of diminishing sensitivity, i.e. the psychological impact of a marginal change decreases as one moves further away from a reference point. This principle implies a probability weighting function that is steep near the reference points, naturally taken to be impossibility and certainty, and relatively flat in the middle.1 However, there is vast individual heterogeneity in the specific shape of the probability weighting function. So far, little is known about factors driving the curvature of the probability weighting function, let alone about determinants of individual differences. One exception is the decision maker’s gender: On average, women’s probability weighting curves depart more strongly from linear weighting than do men’s curves (Bruhin et al., 2010).

Several generalizations of expected utility theory offer a rationale for the shape of the probability weighting function by invoking anticipated emotions (Bell, 1982, Loomes and Sugden, 1986, Gul, 1991, Wu, 1999). Recently, for instance, Walther (2003) has shown that an S-shaped transformation of probabilities may result if decision makers anticipate elation or disappointment at the time when uncertainty is resolved. His model of affective utility predicts that higher sensitivity to anticipated emotions leads to greater departures from linear probability weighting.2

While anticipated emotions have been integrated into economic models of behavior under risk, this is not the case for incidental emotions, like mood states or emotions carried over from recent experiences, which have no causal link to the decision at hand. In the psychology literature, there is a large body of empirical evidence on the effects of incidental emotions on judgment and decision making (Loewenstein and Lerner, 2003, Pham, 2007). Numerous studies show that incidental mood states generally have mood-congruent effects on perception and object valuation. Risks are perceived to be higher under negative moods than under positive moods (Johnson and Tversky, 1983, Wright and Bower, 1992).3 In these studies, probabilities are typically not presented as objective numbers but have to be assessed subjectively. Wright and Bower (1992) also detected a susceptibility effect. When judging more frequently occurring events participants exhibit higher susceptibility to mood states than when judging less frequent ones.

It is an open question whether these results on probability assessment carry over to the valuation of risky prospects with stated objective probabilities. If so, risk preferences may be less stable than assumed by economic theory, and subject to factors completely irrelevant to the decision at hand. The experimental literature reports that subjects often choose differently when confronted with the same decision problems at different occasions. The percentage of subjects with preference reversals has been found to be quite substantial (Hey and Orme, 1994). While many authors would attribute this phenomenon to errors, some of this variation could well be due to sensitivity to incidental emotions.

Whereas studying mood and affect has a long tradition in psychology, economists have only recently become interested in this field of research. Examples of experimental work include Capra (2004) and Kirchsteiger et al. (2006), both of which show significant effects of mood state on behavior in games. If incidental mood also influences decisions under risk, the effect could work via two pathways. Mood states could either affect the valuation of monetary outcomes or probability weighting or both. We conjecture that, in the context of financial decision making, the valuation of monetary outcomes is less susceptible to incidental affect than are probability weights. This hypothesis seems particularly plausible in the light of experimental evidence showing that probability weights seem to be the more malleable component of risk taking attitudes (Fehr-Duda et al., 2010, Abdellaoui et al., in press). We therefore hypothesize that people in good moods should weight probabilities more optimistically, i.e. they should put a relatively higher weight on gain probabilities and a relatively lower weight on loss probabilities, than do people in a neutral state.

This paper addresses the question of individual mood effects by estimating the parameters of a sign- and rank-dependent decision model. We elicited certainty equivalents of a large number of lotteries involving real gains and losses, which enabled us to estimate individual probability weighting functions. Mood states were accounted for by a binary variable indicating whether subjects reported to be in a better than usual mood or not.

To our knowledge, this is the first experimental study that sheds light on individual differences in probability weighting.4 In particular, we show that incidental feelings may have an effect on decision making under risk, rendering risk preferences potentially susceptible to factors irrelevant to the decision at hand. Even though there is no significant gender difference in reported mood states, we find a substantial gender effect in sensitivity to self-reported good mood: Our findings indicate that, in support of our conjecture, women in a better than normal mood tend to weight probabilities more optimistically. No such effect can be detected in average men’s behavior. This finding can be explained by two factors: First, contrary to women, a considerable percentage of men use expected values as a guideline to decision making, which seems to immunize them against mood states. Moreover, we show that these men’s behavior is indeed consistent with expected value maximization. Hence, the gender difference in decision strategy may also explain why the average male probability weighting curve departs less strongly from linear weighting than does the female one. Second, men who do not apply this decision rule behave congruently with good mood, but to a much lesser degree than do women.

The paper is structured as follows. Section 2 explains the experimental design and procedures. After analyzing the raw data in Section 3, the econometric model for estimating the risk parameters is specified in Section 4. Section 5 presents our results, followed by a general discussion in Section 6.

Section snippets

Experimental design and data

In the following section we describe the experimental setup and procedures.5 We recruited 107 students, 58 men and 49 women, of various fields at the University of Zurich and the Swiss Federal Institute of Technology Zurich. From each subject, we elicited certainty equivalents for 50

Descriptive analysis

Observed risk taking behavior can be conveniently summarized by relative risk premia RRP=(evce)/|ev|, where ev denotes the lottery’s expected value and ce stands for the observed certainty equivalent. RRP > 0 indicates risk aversion, RRP < 0 risk seeking, and RRP = 0 risk neutrality. Fig. 1 exhibits median risk premia sorted by the probability of the lotteries’ highest gains or losses, respectively. Median RRP s display the familiar fourfold pattern of risk attitudes: subjects are risk averse for

Econometric model

One objective of the current paper is disentangling the effect of mood state on outcome valuation from its effect on probability weighting. For this purpose we use an econometric model consisting of three components. First, we describe the behavioral model, i.e. our assumptions on how individuals evaluate risky prospects. Second, we specify the relationship between the parameters of the behavioral model and the variables that presumably influence the magnitude of these parameters. Third, in

Model selection

Estimating the econometric model by maximum likelihood yields estimates for the coefficients of the explanatory variables θˆk and, in turn, for the parameters of the value and the probability weighting functions. As the descriptive analysis has shown, risk taking behavior is significantly associated with GOODMOOD, albeit only for women. With the parameter estimates at our disposal, we are now able to answer the question whether good mood affects the valuation of monetary outcomes or probability

Discussion

Imagine you are facing a risky decision and assess all your options. Should how your day has been going so far color your judgment? Presumably, you will answer in the negative as would probably most people. However, we find strong evidence that people’s risk taking behavior is susceptible to incidental affect and that this susceptibility is more pronounced for women. Women who report that their day has been going better than usual exhibit two kinds of behavioral effects: First, they weight

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      Such decisions are significantly influenced by one’s emotions. People feeling positive emotions may be relatively optimistic, so that they may fixate on positive rather than negative outcomes, and therefore take on greater risk than they would otherwise (e.g., Grable and Roszkowski, 2008; Fehr-Duda et al., 2011; Kuhnen and Knutson, 2011; Bassi et al., 2013; Halko et al., 2015; Dalton et al., 2020). On the other hand, positive emotions have also been linked to enhanced cognitive ability, productivity, patience, and healthy eating behavior (Erez and Isen, 2002; Isen, 2008; Fedorikhin and Patrick, 2010; Ifcher and Zarghamee, 2011).

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    This research was supported by the Swiss National Science Foundation, Grant #100012-109907. A previous version, titled “Risk and Rationality: The Effect of Incidental Mood on Probability Weighting”, is available at http://www.soi.uzh.ch/research/wp/2007.html.

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