Ambiguity Aversion , Comparative Ignorance , and Decision Context

People typically find bets less attractive when the probability of receiving a prize is more vague or ambiguous (Ellsberg, 1961). According to Fox & Tversky’s (1995) comparative ignorance hypothesis, ambiguity aversion is driven by the comparison with more familiar events or more knowledgeable individuals, and diminishes or disappears in the absence of such a comparison. In this paper we emphasize that “comparative ignorance” refers to the state of mind of the decision maker. We extend the comparative ignorance hypothesis by documenting four new ways in which decision context can affect willingness to act under uncertainty that do not rely on the comparative-noncomparative evaluation paradigm that was used in previous studies. First, people find uncertain bets more attractive when preceded by questions about less familiar items than when preceded by questions about more familiar items. Second, the preference to bet on more familiar domains is less pronounced for the first domain evaluated on a survey than for later domains. Third, people find bets less attractive when they are provided with diagnostic information that they do not know how to use, compared to when they are provided with no such information. Finally, people are sensitive to the relative competence of their counterpart when playing a simple competitive (“matching pennies”) game, but not when playing a noncompetitive (coordination) game that has the same mixed strategy Nash equilibrium. Key words: ambiguity aversion, uncertainty, context, comparative ignorance, competence Ambiguity and Context page 3 Ambiguity Aversion, Comparative Ignorance, and Decision Context Most choices in life have uncertain consequences. Decisions to undergo surgery, invest in a mutual fund, or purchase insurance must be made without knowing in advance whether the operation will be successful, the fund will outperform the market, or there will be a need to make a claim on the policy. Occasionally, the decision maker knows precise probabilities of potential outcomes. For instance, a gambler in a Monte Carlo casino might recognize that the probability of a roulette wheel landing “red” is 18/37; a patient in a health clinic might be told that 1 in 40,000 people inoculated for measles experiences an adverse reaction. More often, however, decision makers are required to judge the likelihood of relevant events for themselves based on computation, intuition, and/or hearsay, with some degree of imprecision or vagueness. This contrast between clear and vague probabilities was first discussed by Knight (1921), who distinguished between risk, which can be represented by precise probabilities, and (unmeasurable) uncertainty, which cannot. He argued that entrepreneurs earn economic rents for bearing uncertainty. Meanwhile, Keynes (1921) distinguished between judged probability, which represents the balance of evidence in favor of a particular proposition, and the weight of evidence, which represents the quantity of evidence supporting that balance. Keynes asserted that people should be more willing to bet on probabilities that are supported by a higher weight of evidence. Ambiguity and Context page 4 The contrast between clear and vague probabilities was disregarded by later theorists. Subjectivists (e.g., Ramsey, 1931) have argued that degree of belief should be measured by preference between bets, and thereby assumed that vagueness does not influence choice independently of belief strength. Although Savage (1954) explicitly addressed the topic of vague probabilities, he dismissed its relevance to choice in his development of subjective expected utility theory (pp. 57-60). Interest in the problem of vague probabilities was revived by Ellsberg (1961), who argued that people generally prefer to bet on known rather than unknown probabilities. Ellsberg’s simplest demonstration involves two urns, each containing 100 balls. The first urn contains 50 red balls and 50 black balls, whereas the second contains red and black balls in an unknown proportion. When asked to bet on a blind draw from an urn, most people express no particular color preference, but they would rather bet on the clear (5050) urn than on the vague urn. This pattern of preferences violates expected utility theory because the subjective probabilities of red and black, derived from preferences, cannot sum to one for both urns. Ellsberg’s own interpretation was that in addition to the utility of outcomes and the probability of events determining them, decision makers consider a “third dimension,” which he called ambiguity, defined as “a quality depending on the amount, type, and ‘unanimity’ of information, and giving rise to one’s degree of ‘confidence’ in an estimate of relative likelihoods” (p. 657). Thus, Ellsberg drew a distinction between judgment and willingness to act: “An individual... can always assign relative likelihoods to the states of nature. But how does he act in the presence of uncertainty? The answer to that may depend on Ambiguity and Context page 5 another judgment, about the reliability, credibility, or adequacy of his information.” (p. 659) The preference to bet on clear rather than vague probabilities has been demonstrated in numerous studies using variations of Ellsberg’s original paradigm. Researchers have typically operationalized and modeled the degree of ambiguity as the range or variance of the second-order probability distribution, interpreting ambiguity aversion as a reluctance to bet on vaguer probabilities (for a comprehensive review of this literature, see Camerer & Weber, 1992). A more recent stream of research emphasizes instead the decision maker’s confidence in his or her knowledge or information (e.g., Frisch & Baron, 1988; Heath & Tversky, 1991). In particular, Heath and Tversky (1991) conducted a series of experiments comparing people’s willingness to bet on their uncertain beliefs with their willingness to bet on chance events. Contrary to the ambiguity aversion hypothesis, they found that people prefer to bet on their vague beliefs in situations where they feel especially competent or knowledgeable, though they prefer to bet on chance when they do not. In one test of Heath and Tversky’s competence hypothesis, participants were asked to choose among bets involving three sources of uncertainty: the winner of professional football games, the winner of various states of the 1988 presidential election, and the results of random draws from an urn containing a known proportion of winning balls. Participants who said they knew a great deal about football and little of politics preferred betting on football games rather than on chance events that they considered equally probable. However, these participants preferred betting on chance events rather than on political events that they considered equally probable. Analogously, participants who Ambiguity and Context page 6 knew a great deal about politics and little of football exhibited the opposite pattern, preferring politics to chance and chance to football. The preference to bet on more familiar sources of uncertainty has since been replicated in a number of studies (e.g., Taylor, 1995; Tversky & Fox, 1995; Keppe & Weber, 1995; Taylor & Kahn, 1997). It may provide a partial explanation for the commonly observed preferences to invest in the domestic stock market over foreign markets (see e.g., French & Poterba, 1991; Kilka & Weber, 2001) and the telephone company in one’s home state over other states (Huberman, in press). The competence hypothesis suggests that ambiguity aversion (or, more generally, “source preference”) is governed by the decision maker’s appraisal of his or her knowledge of relevant events rather than some second-order measure of probability vagueness. Furthermore, Fox and Tversky (1995) argued that perceived competence only affects decisions to the extent that this dimension is brought to mind. According to their comparative ignorance hypothesis, ambiguity aversion is driven by a comparison with more familiar sources of uncertainty or more knowledgeable people (which makes the notion of competence more salient), and is not as pronounced in the absence of such a comparison (where the notion of competence is less salient). This represents a sharp break from previous accounts of decision under uncertainty because it asserts that decisions are influenced by the cognitive context in which the decision maker finds him or herself so that a particular uncertain prospect may be more or less attractive depending on whether or not a contrasting state of knowledge is salient. Ambiguity and Context page 7 Virtually every empirical study of ambiguity aversion and competence effects reported before 1995 relied on a within-subject design in which all participants evaluated multiple sources of uncertainty. In several experiments, Fox and Tversky (1995) documented ambiguity aversion in comparative contexts in which each participant evaluated lotteries with both clear and vague probabilities (a within-subject design), but found that the effect was greatly diminished or disappeared entirely in noncomparative contexts, in which different participants evaluated each lottery in isolation (a betweensubject design). Additionally, these researchers showed that participants who were told that more knowledgeable people would be making the same choice were much less likely to bet on their prediction than participants who were not told about such experts. Further evidence from market studies has shown that the pronounced difference in prices for clear versus vague bets, observed when both bets are traded together, diminishes or disappears entirely when these bets are traded in separate markets (Sarin & Weber, 1993). Chow and Sarin (1999) have obtained data that lend further credence to the comparative ignorance hypothesis. First, they replicated the finding that the preference for known probabilities over unknown probabilities diminishes in the absence of an explicit comparison between sources of uncertainty, though in the studies that they report the preference persists even in non-comparative settings (see Chow & Sarin, 2001).1 Second, they found that the preference for known over unknown probabilities is amplified when participants are made aware of the fact that another participant or group of participants is evaluating the other kind of bet. Third, participants preferred betting on known probabilities to betting on so-called “unknowable” probabilities (i.e., in which probabilities are presumably unknown to anyone), and they preferred betting on Ambiguity and Context page 8 “unknowable” probabilities to betting on “unknown” probabilities (i.e., in which they are told that another person knows the relevant probability). It is important to emphasize, as Fox & Tversky (1995, p. 599) did, that the distinction between comparative and noncomparative assessment refers to the state of mind of the decision-maker rather than the experimental manipulation of context. We suggest two important corollaries to the comparative ignorance hypothesis: (1) any feature of the decision context that makes a contrasting state of knowledge more salient should exacerbate source preferences; and (2) source preferences are inherently relative so that absolute willingness to act under uncertainty depends on the particular standards of comparison that are available to the decision maker. Note that Fox and Tversky (1995) and Chow and Sarin (1999) demonstrated comparative ignorance effects by juxtaposing a familiar prospect with an unfamiliar prospect or by explicitly mentioning other people who are more (or less) knowledgeable. The present observations suggest that one can produce comparative ignorance effects through a broader array of experimental manipulations. The purpose of this paper is to provide more general support for the comparative ignorance hypothesis using four novel manipulations of decision context that do not rely on the comparative-noncomparative elicitation paradigm. In particular, we demonstrate comparative ignorance effects (1) within an entirely comparative context, (2) in a context that shifts from noncomparative to comparative, (3) within an entirely noncomparative context, and (4) in a strategic (interactive) context. In a first set of studies, all participants are reminded of contrasting states of knowledge (i.e., the context is comparative for all participants) yet the specific nature of Ambiguity and Context page 9 this comparison varies by condition. Here we argue that a participant’s relative rather than absolute degree of perceived competence will govern her willingness to bet. In a second set of studies, all participants evaluate a relatively clear and relatively vague source of uncertainty, but the order in which sources are presented varies by condition. Here we argue that the context shifts from noncomparative for the first source to comparative for the second source so that the salience of contrasting states of knowledge is higher when evaluating the second source than when evaluating the first source. In a third set of studies, all participants encounter a noncomparative context, but we attempt to make a superior state of knowledge more salient by providing diagnostic information that only an expert could use to forecast relevant outcomes. Here we predict that the addition of such information will make most of our naïve participants less willing to bet. In a final study, we explore comparative ignorance effects in the context of simple strategic interactions. Here we argue that the relative competence of one’s counterpart should be especially salient and therefore influence choices. We conclude with a discussion in which we summarize the present results, discuss related work, suggest potential applications, and articulate possible directions for future research. Comparative ignorance in a comparative context Fox and Tversky (1995) argued that ambiguity aversion is driven by the contrast between a person’s limited knowledge about an event and his or her superior knowledge about another event. However, these authors remain agnostic concerning: (1) the extent to which comparison enhances the attractiveness of the more familiar bet versus the extent to which it diminishes the attractiveness of the less familiar bet; and (2) the extent to which the specific nature of the contrast affects willingness to act. It could be, for Ambiguity and Context page 10 example, that a bet’s attractiveness is governed by a person’s absolute degree of knowledge—but only when that knowledge is made salient by any sort of contrast. It seems more plausible, however, that a person’s assessment of her degree of competence or incompetence is itself an inherently relative construct. Just as a baseball batting average is meaningless in the absence of a standard of comparison (to a reference group and/or one’s past performance), other measures of competence often depend on the specific object of comparison. When a person is reminded of more familiar domains or people with greater knowledge or skill, she will feel relatively incompetent; when she is reminded of less familiar domains or people with lesser knowledge or skill, she will feel relatively competent. This account predicts that within a comparative decision context, people will value an uncertain prospect more highly when they are reminded of an inferior state of knowledge than when they are reminded of a superior state of knowledge. The first two studies test this hypothesis. Study 1 We recruited 110 law students at Willamette University, which is located in Salem, Oregon. Participants completed a one-page survey in a classroom setting for which they received no compensation. We presumed that these students would be highly familiar with Salem weather, moderately familiar with the weather in San Francisco, and relatively unfamiliar with the weather in Istanbul, Turkey. We asked participants how much they would be willing to pay to bet on each side of a proposition that offered a fixed prize if the temperature in a particular city were above or below a specified value. The exact wording was as follows: Ambiguity and Context page 11 Imagine that you have been offered a ticket that will pay you $100 if the afternoon high temperature in {CITY} is at least 65 degrees Fahrenheit one week from today. What is the most you would be willing to pay for such a ticket? The most I would be willing to pay is $ ________ Imagine that you have been offered a ticket that will pay you $100 if the afternoon high temperature in {CITY} is less than 65 degrees Fahrenheit one week from today. What is the most you would be willing to pay for such a ticket? The most I would be willing to pay is $ ________ Approximately half the respondents priced prospects based on Salem temperature followed by prospects based on San Francisco temperature; the remaining respondents priced prospects based on Istanbul temperature followed by prospects based on San Francisco temperature. The order of complementary prospects (at least 65 degrees/less than 65 degrees) was otherwise counterbalanced. According to the present account, San Francisco bets should be more attractive when they are preceded by the relatively unfamiliar Istanbul bets than when they are preceded by the relatively familiar Salem bets. Eleven participants who violated stochastic dominance or neglected to answers all of the questions were excluded from the analysis. Let c(SFist ≥ 65) denote willingness to pay for the prospect that offers $100 if the temperature in San Francisco is at least 65 degrees one week in the future, where this prospect follows prospects contingent on future temperature in Istanbul. For each respondent we added his willingness to pay for complementary bets. Mean sums are listed in Table 1 (with standard errors in parentheses). For instance, the lower left cell presents the mean value of c(SFsal < 65) + c(SFsal ≥ 65). Results support our prediction. Respondents were willing to pay an average of $16.18 more to bet on San Francisco temperature in the condition in which they were made to feel relatively competent (Form B) compared to the condition in which Ambiguity and Context page 12 they were made to feel relatively incompetent (Form A), an increase of 74% (t(97) = 2.88; p < .005, one-tailed). ----------------------------------------------INSERT TABLE 1 ABOUT HERE ----------------------------------------------The same pattern holds for the individual bets. Participants priced the prospect that offered “$100 if… San Francisco is… less than 65 degrees…” higher when this bet followed the (unfamiliar) Istanbul prospects than when this prospect followed the (familiar) Salem prospect, c(SFist < 65) = 16.62, and c(SFsal < 65) = 11.42 (t(97) = 1.60, p < .06). Similarly, c(SFist ≥ 65) = 21.54, and c(SFsal ≥ 65) = 10.51 (t(97) = 3.31, p < .001). Note that respondents were willing to pay no less to bet on the unfamiliar Istanbul than they were willing to pay to bet on the familiar Salem (t(97) = -1.01, n.s.). This result is consistent with the comparative ignorance hypothesis if one assumes that the first item on the survey was evaluated in a noncomparative manner. We will have more to say about such order effects in the next section of this paper.