Playing for peanuts: Why is risk seeking more common for low-stakes gambles?

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Abstract

Previous research has found that decision makers are more risk seeking for small-stakes gambles than for large-stakes gambles. This “peanuts effect” is not easily explained by Prospect Theory. Two experiments examined the range of circumstances in which peanuts effects occur and tested the hypothesis that anticipated disappointment or anticipated regret explains the peanuts effect. The results suggest that the peanuts effect is related to disappointment, but do not support a connection between the peanuts effect and regret.

Introduction

Generally speaking, decision-makers prefer not to take chances. Given the choice between playing a gamble and receiving the expected value of the gamble, most decision-makers choose the latter. This risk-aversion is a very common and robust phenomenon; Kahnman and Tversky once called the tendency to be risk-averse “perhaps the best known generalization regarding risky choices” (Kahneman & Tversky, 1979).

There are, however, exceptions to this general rule. The tendency of decision-makers to be risk-averse is widespread, but applies only when the outcomes concerned are gains. When faced with a potential loss, decision-makers tend to be risk seeking—that is, given the choice between a possibility of loss and a certain loss with the same expected value, they prefer the risky option (Kahneman and Tversky, 1979, Markowitz, 1952).

Another example of risk-seeking behavior was first noted by Markowitz (1952). Consider a choice between $0.10 for certain and a 10% chance of winning $1. A risk-averse decision-maker would choose the $0.10 for certain; however, Markowitz believed, quite plausibly, that most people presented with such a small-stakes choice would prefer the gamble for $1. We can continue working our way up the payout scale with similar choices: what about a choice between $1 and a 10% chance of $10? Between $10 and a 10% chance of $100? Markowitz proposed that for each person there comes a point where his or her preferences reverse. I might prefer to take a 10% chance of $100 over $10 for sure, but given the same choice at a higher monetary level, I would choose $100 for certain over a 10% chance of $1000 (Markowitz, 1952).

Note that in both cases, I am being asked to accept 10 times the risk in exchange for 10 times the money, yet I do not make the same choice in both circumstances. I am more risk-averse for small gains than for large ones. (In fact, in Markowitz’s example I am actually risk-seeking for very small gains.) The effect of decreasing risk aversion with decreasing monetary amounts was christened the “peanuts effect” (Prelec & Loewenstein, 1991)—decision-makers are more willing to take risks when playing for “peanuts.” (By this definition, it is not actually necessary to become risk-seeking for very small gains, merely to become less risk-averse for smaller payouts.) Markowitz also suggested that the peanuts effect is reflected in the domain of losses: that decision makers are more risk seeking for small losses than for large losses.

Although Markowitz himself did not test his effect experimentally, a number of subsequent demonstrations of the peanuts effect exist. Green, Myerson, and Ostaszewski (1999) determined subjects’ indifference points through a series of choices, and found subjects to be less risk-averse for small gain amounts than large ones. Green, Myerson, and colleagues have also demonstrated the peanuts effect in other experiments. (Du et al., 2002, Holt et al., 2003, Myerson et al., 2003). Rachlin, Brown, and Cross (2000) found subjects to be less risk averse for small amounts than for large amounts when making a graphical rating response, but did not find the same pattern for choice responses. Hershey and Schoemaker (1980) asked subjects a series of risky choice questions and found a peanuts effect in the domain of gains and a reflected peanuts effect in the domain of losses. Hogarth and Einhorn (1990) asked subjects to chose between and rank options, and found a peanuts effect for both gains and losses, using both hypothetical and real payouts. In a meta-analysis of published Asian-disease framing effects problems, Kühberger, Schulte-Mecklenbeck, and Perner (1999) found a peanuts effect for a gains frame, but not for a losses frame. Casey, 1991, Casey, 1994 has demonstrated the peanuts effect for both bidding and choices.

The peanuts effect can potentially be explained via the utility function. Markowitz explained the peanuts effect by postulating an inflected slope for the utility function of money. In gains, he proposed the utility function is convex for small values and concave for large values. The inflection point of the function represents the magnitude at which the decision-maker switches from risk-seeking to risk-averse behavior. He proposed that in losses the utility function was concave for small losses and convex for large ones. Thus his proposed utility function contains three inflection points: one at the origin and two more representing the monetary points at which behavior switches from being risk seeking to risk averse or vice versa (see Fig. 1).

Under Prospect Theory it is now generally accepted that the utility function for gains is everywhere concave and for losses everywhere convex (Kahneman and Tversky, 1979, Tversky and Kahneman, 1992) (see Fig. 2). This is inconsistent with Markowitz’s original postulate that decision-makers are actually risk-seeking for small amounts of money, which requires a convex utility function. However, it is not inconsistent with the more commonly used definition of the peanuts effect suggested by the previous experimental data: that decision-makers are less risk averse for small gain amounts than large ones. This behavior would be consistent with a concave utility function that is almost linear (approaching risk neutrality) near the origin but gets more curved as payout amounts increase. Thus, initially it seems that the peanuts effect is not inconsistent with Prospect Theory.

Examination of a similar bias in the domain of intertemporal choice casts some doubt on the ability of Prospect Theory to explain the peanuts effect. The magnitude of a payout influences time preferences as well as risk preferences. Time preferences reflect preferences for the timing of a delayed outcome and can be quantified as the percentage increase in value needed to offset a given delay. When given the choice between $10 now and $20 in 1 year, for example, many decision-makers may prefer to receive $10 now, indicating that more than a doubling of value would be needed to compensate for the 1-year delay. However, given a choice between $100 now and $200 in 1 year, the delayed $200 becomes the more preferred option, now indicating that less than a doubling of value is needed to compensate for the 1-year delay. Thus, decision makers tend to have a more positive time preference for small magnitude outcomes than for large magnitudes (e.g., Chapman, 1996; Chapman & Winquist, 1998; Thaler, 1981).

The magnitude effect is similar to the peanuts effect in all respects but one: the two effects run in opposite directions if risk seeking corresponds to greater willingness to wait for an outcome, as is usually assumed. This poses a problem for attempts to develop a common explanation for effects of risk and delay, something that has been proposed by numerous researchers (e.g., Keren and Roelofsma, 1995, Prelec and Loewenstein, 1991, Rachlin et al., 1986, Rachlin et al., 1991). Both Green, Myerson, and colleagues (Du et al., 2002, Green et al., 1999, Holt et al., 2003, Myerson et al., 2003) and Rachlin et al. (2000) have found the magnitude effect and peanuts effect in the same experiment and both noted the problems this entails for any attempt to reduce the effects of risk and delay to a common psychological mechanism. Prelec and Loewenstein (1991) have noted this difficulty as well.

The existence of the magnitude effect also poses a serious problem for a utility function explanation of the peanuts effect. The magnitude effect requires a utility function that increases in proportional sensitivity (Prelec & Loewenstein, 1991). That is, the ratio between the utilities of two monetary values with constant ratio must increase as the monetary values increase. In the example above, decision-makers appear to view the ratio between the utilities of $100 and $200 as psychologically larger than that between the utilities of $10 and $20—thus they are willing to wait a year for the former increase, but not the latter. However, the peanuts effect demands a utility function that decreases in proportional sensitivity. The ratio between the utilities of $100 and $200 must be psychologically smaller than that between the utilities $10 and $20 to explain why subjects would be less willing to take risks to obtain the former increase than the latter.

Neither the magnitude effect nor the peanuts effect is in principle non-normative, since either could be explained under Expected Utility Theory by the shape of the utility function. Either can be explained under Prospect Theory, also by the shape of the utility function. However, they cannot both be explained by the shape of the utility function, as the two effects require utility functions with opposing properties.

If the utility function cannot explain both the peanuts and magnitude effects, what can? The differing directions of the peanuts and magnitude effect suggest that some factor that applies only to risk (or only to time) is at work. Prelec and Loewenstein (1991) suggest that the explanation for the peanuts effect may lie in the realm of disappointment.

When picking a 10% chance of $1 over $0.10 for sure, one is inclined to think, “Who cares if I pick the gamble and lose? I’m only passing up 10 cents!” Passing over a chance to receive a dime is no big deal. However, giving up $1000 for sure, even in exchange for a 10% chance of $10,000, is likely to give one pause. What happens if I choose the gamble? It’s likely I’ll lose and be unhappy that I could have had $1000 but wound up with nothing instead.

According to decision affect theory (Mellers, Schwartz, Ho, & Ritov, 1997), negative emotions resulting from decision outcomes take two forms. Disappointment is the emotion experienced when a different state of the world would have produced a better result. If I am offered a 10% chance of winning $10,000 and lose the gamble, I will be disappointed that I didn’t win (Bell, 1985, Loomes and Sudgen, 1986). Regret is the emotion experienced when a different choice on the part of the decision-maker would have produced a better result. Suppose I am asked to choose between $1000 for sure and a 10% chance of $10,000. I choose to take the 10% chance of $10,000 and lose the gamble, ending up with nothing. Now I still feel disappointed that I didn’t win, but I also feel regret over choosing the gamble instead of $1000 for sure (Bell, 1982, Loomes and Sudgen, 1982). In a nutshell, disappointment means wishing things had turned out differently; regret means wishing one had made a different choice.

Disappointment theory defines disappointment as a function of the difference between the actual outcome and the expected value of the gamble (Bell, 1985, Loomes and Sudgen, 1986); regret theory defines regret as a function of the difference between the outcome of the chosen option and the outcome of the foregone option (Bell, 1982, Loomes and Sudgen, 1982). Therefore, both theory and intuition imply that disappointment and regret are smaller, and thus play a smaller role, in small-stakes decisions than in large-stakes ones. No one is likely to be disappointed when they gamble on a 10% chance of $1 and lose, or regret not choosing to accept a certain $0.10 instead. Because the expected values of both gambles are very small, when I lose the gamble and receive nothing, the resulting regret or disappointment is very small as well. Therefore, disappointment and regret may not be major factors in these small-outcome gambles. Decision makers can afford to take risks when playing for peanuts, as they know they will not feel very much regret or disappointment about the outcome. In contrast, for large-stakes gambles, where regret and disappointment are much larger, the anticipated negative affect may drive them to be more risk-averse.

Thus, disappointment, regret, or some combination could well explain the peanuts effect. Generally, avoiding disappointment or regret drives people to more risk-averse decisions. If disappointment and regret play little role in decisions with small outcomes, decision makers will be more risk-seeking for these small outcomes than when making decisions for larger outcomes which do involve the possibility of significant disappointment or regret.

If disappointment is responsible for the peanuts effect, it could also explain why the magnitude and peanuts effect run in opposite directions. By definition, disappointment occurs when a different state of the world would have produced a better outcome. This can only occur if there are multiple possible states of the world with regards to the outcome in question—in other words, if the outcome is risky. A certain outcome has no alternate possible states of the world and thus no potential for disappointment. Because the magnitude effect involves certain outcomes, the choices that produce it are free of the possibility of disappointment. A decision-maker whose utility functions displays increasing proportional sensitivity could then show both the magnitude effect and the peanuts effect: the magnitude effect produced by the underlying utility function, and the peanuts effect produced by the differential levels of disappointment incurred by outcomes of different sizes. Although such a utility function would by itself result in the opposite of the peanuts effect, instead the peanuts effect occurs because of the influence of disappointment the domain of risky choice.

The question of regret and the magnitude effect is more complicated. Regret is experienced when a decision maker feels that a different choice would have produced a better outcome (Gilovich & Medvec, 1995), and this could occur in both risky choice and intertemporal choice. For example, a dieter may impulsively eat two pieces of cheesecake, but regret the choice the next morning when he steps on the scale. In fact, he may eat the cheesecake even though he knows he will regret it later because the present utility of the cheesecake outweighs the future utility of losing weight—and the future disutility of the anticipated regret.

Notice what happens as anticipated future regret increases. Eventually, the disutility of the regret associated with making an impulsive choice becomes large enough that the discounted future regret outweighs the appeal of the impulsive option. Thus, as anticipated regret increases, the willingness to wait for a future outcome should increase as well. This is precisely what occurs in the magnitude effect in intertemporal choice. As the size of the outcome increases, and with it the associated regret, decision-makers become less impulsive and more willing to wait. Regret can therefore potentially explain the differing directions of the peanuts and magnitude effect, as any influence of anticipated regret would drive the two effects in different directions.

One complication to a regret account of the peanuts effect is the issue of feedback. According to the original Regret Theory, feeling regret requires knowing what the outcome of the forgone choice would have been, allowing easy comparison between the obtained and unobtained outcomes. However, experiments involving choices between gambles usually tell the subject nothing about the result of the gamble not chosen—including studies that have demonstrated the peanuts effect. If there can be no regret without anticipated feedback then regret cannot be the explanation for the peanuts effect.

However, if regret depends on feedback it is not particularly useful for explaining real-world decision making either. Although sometimes we learn the outcome of foregone options, usually we will never know what would have happened if we would married our high school sweethearts (or failed to marry them), but it seems unreasonable to suggest that we cannot regret our choice if the outcome we did obtain was unfavorable.

Empirically, the evidence for regret in the absence of feedback is mixed. Some studies suggest it does not occur (e.g., Mellers, Schwartz, & Ritov, 1999) and others have found that that it does (e.g., Bar-Hillel and Neter, 1996, Zeelenberg et al., 1998). Faced with mixed evidence it seems reasonable to take the suggestion of Zeelenberg (1999) and assume that regret is weaker but not absent when decision-makers receive no feedback about the unobtained outcome. If this is the case, regret could be an explanation for the peanuts effect.

Disappointment and regret are negative emotions associated with decisions with outcomes that were less than ideal. However, decisions can also have positive outcomes and the emotions associated them can likewise be positive. The disappointment one feels after losing a gamble goes hand and hand with the elation one feels after winning; regret over making a choice that resulted in a poorer outcome turns into rejoicing when the choice you made proves to be the optimal one.

It is possible that when making decisions, decision makers seek to experience elation and rejoicing as well as to avoid disappointment and regret. However, such behavior cannot explain the peanuts effect: like disappointment and regret, elation, and rejoicing increase as the size of the payout increases. The desire to experience elation and rejoicing would therefore drive decisions in the opposite direction of that seen in the peanuts effect: as the payouts increase, the potential for elation and rejoicing increases and we would expect to see subjects become more risk seeking for larger payouts, not more risk averse as seen in the peanuts effect. Therefore we concentrate on disappointment and regret in the present studies.

The purpose of the present experiments is twofold. First, few studies have been conducted specifically to investigate the peanuts effect since it was first proposed by Markowitz in 1952 (e.g., Du et al., 2002, Holt et al., 2003, Hogarth and Einhorn, 1990; Green et al., 1999; Myerson et al., 2003, Rachlin et al., 2000). To our knowledge, no investigation of the peanuts effect has extended far beyond the observation that it exists, and factors that moderate the peanuts effect have not been examined in a systematic fashion. Experiment 1 in the current paper addresses this deficit by examining when a peanuts effect is obtained and what factors influence its size and presence. This experiment provides an initial test of whether the peanuts effect can be explained by any utility function. It also examined what factors produce sizable peanuts effects so that appropriate stimuli could be chosen for future experiments. Experiment 2 provided an additional test of whether the peanuts effect can be explained by the shape of the utility function and contrasted this account with an alternative hypothesis that disappointment and/or regret are responsible for the peanuts effect.

Section snippets

Experiment 1: Payouts and probabilities

The purpose of Experiment 1 was to explore the influence of a variety of factors on the peanuts effect, with an eye towards finding values that would produce large peanuts effects for use in future experiments. Subjects made choices between gamble pairs. Each gamble had one positive and one zero outcome. The two gambles in a choice pair had the same expected value, but one was riskier than the other. Compared to the less risky gamble, the riskier gamble had a higher positive outcome and lower

Experiment 2: Regret, disappointment, and loss

In Experiment 1, we established sets of gambles that yielded a strong peanuts effect. In Experiment 2, we used this information to study the impact of disappointment and regret on the peanuts effect. Additionally, Experiment 2 tested whether a reflected peanuts effect occurred in the domain of losses.

Consider opening a soft drink bottle with the advertisement, “Find the winning game piece to win a new car!” Opening the bottle, you find “Sorry, you are not a winner” written under the lid. Are

General discussion

The peanuts effect is not a well-understood or well-studied phenomenon. The current studies provide evidence as to the conditions under which the phenomenon occurs and the psychological factors that may produce the effect.

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    This research was supported by an NSF graduate fellowship to the first author and NSF grant SES 99-75083 to the second author.

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