The Description–Experience Gap in Risky and Ambiguous Gambles

Recent research in decision making reported a description–experience (DE) gap: opposite risky choices when decisions are made from descriptions (gambles in which probability distributions and outcomes are explicitly stated) and when decisions are made from experience (the knowledge of the gambles is obtained by sampling outcomes from unknown probability distributions before making a choice). The DE gap has been reported in gambles commonly involving a risky option (outcomes drawn from a fixed probability distribution) and a safe option (probability of the outcome is 1), or in gambles involving two risky options. Here, we extend the study of the DE gap to gambles in which people choose between a risky option and an ambiguous option (with two nested probability distributions, where the eventgeneration mechanism is more opaque than that in the risky option). We report empirical evidence and show a DE gap in gambles involving risky and ambiguous options. Participants’ choices are influenced by the information format and by the ambiguous option: participants are ambiguity-seeking in experience and ambiguity-averse in description in problems involving both gains and losses. In order to find reasons for our results, we investigate participants’ sampling behavior, and this analysis indicates choices according to a cognitive model of experiential decisions (instance-based learning). In experience, participants have small sample sizes, and participants choose options where high outcomes are experienced more frequently than expected. We discuss the implications of our results for the psychology of decision making in complex environments. Copyright © 2013 John Wiley & Sons, Ltd. key words risk; ambiguity; instance-based learning theory; decisions from experience; ambiguity aversion; complex environments THE DESCRIPTION–EXPERIENCE GAP IN CONDITIONS INVOLVING RISK AND AMBIGUITY Benjamin Franklin famously stated that the only things certain in life are death and taxes. In many decisions we make, we face different options with varying degrees of ambiguity. While we might be able to attach specific probabilities to different outcomes in certain problems (e.g., the probability of getting a “3” when throwing a fair die; Hertwig, in press), we may encounter certain events where assessing a precise probability value is not possible (e.g., when predicting the precise probability of a future global-warming catastrophe; Dutt & Gonzalez, 2012). The economist Frank Knight (1921) made an initial conceptual distinction between decisions under risk (“measurable probabilities”) and decisions under ambiguity (“unmeasurable probabilities”) (p. 20). Therefore, risk refers to decisions where the decision maker knows with certainty the mathematical probabilities of possible outcomes for choice options; in contrast, ambiguity refers to decisions where the likelihoods (probabilities) of different outcomes are vague and cannot be expressed with any mathematical precision (Knight, 1921; Luce & Raiffa, 1957; Rakow & Newell, 2010). For risky decisions, an increasing body of research indicates that choices between options depend on how information about probabilities and outcomes is learned. Researchers have made use of a “sampling paradigm” in decisions made from “experience” where people first sample as many outcomes as they wish from an option with defined probability distributions (that are unknown to participants) and then decide from which option to make a single draw for real (Hertwig, Barron, Weber & Erev, 2004; Hertwig & Erev, 2009). In contrast, when decisions are made from “description,” the information about the possible outcomes from an option and their probability distribution is given to the participants, and they make a selection between different options (Hertwig et al., 2004). In both experience and description, people are asked to either choose between two risky options (each with a single probability distribution) or choose between a risky option and a safe option (where probability = 1). For descriptive decisions, people behave as if rare (low probability) outcomes receive more impact than they deserve according to their objective probability, whereas for experiential decisions, people behave as if rare outcomes receive less impact than they deserve (Gonzalez &Dutt, 2011; Hertwig et al., 2004; Hertwig & Erev, 2009; Weber, Shafir & Blais, 2004). This phenomenon has been called the description–experience (DE) gap in decisions under risk, and it seems to hold for problems involving both gains and losses. Like risk, decisions under ambiguity could also be presented to participants in either a descriptive or an experiential form. However, the probabilities of outcomes in the ambiguous option cannot be expressed with any mathematical precision (Rakow & Newell, 2010), and the question is how to In decisions under risk, the DE gap is defined as participants’ risky choices in experience minus their risky choices in description (Hertwig et al., 2004). *Correspondence to: Varun Dutt, School of Computing and Electrical Engineering, School of Humanities and Social Sciences, Indian Institute of Technology, Mandi, PWD Rest House 2nd Floor, Mandi 175 001, H.P., India. E-mail: [email protected] Copyright © 2013 John Wiley & Sons, Ltd. Journal of Behavioral Decision Making, J. Behav. Dec. Making, 27: 316–327 (2014) Published online 30 October 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/bdm.1808 distinguish ambiguity from risk? One possibility proposed by Arló-Costa and colleagues (Arló-Costa & Helzner, 2009; Arló-Costa, Dutt, Gonzalez & Helzner, 2011) is to distinguish ambiguity from risk in terms of the number of random variables that determine the outcomes, that is, the number of probability distributions needed to determine the outcome of a choice. Typically, in decisions under risk, the outcome of a choice is determined by a single random variable (one probability distribution) (Hertwig & Erev, 2009). However, one way of making the same risky option ambiguous might be to break this single random variable (one probability distribution) into equivalent two nested random variables (two probability distributions), such that the working of both these events now determines the resulting outcome. We refer to conditions in which the outcome of a choice is determined by two or more probability distributions as ambiguous, to distinguish it from risky conditions (one probability distribution) but also to acknowledge that this eventgeneration mechanism is not really an ambiguous one in the Ellsberg sense (see discussion in the following sections) but instead simply more opaque than the one probability distribution risky mechanism. The idea of two or more nested probability distributions in decisions under ambiguity is common in many natural decision making situations (Gonzalez, Vanyukov & Martin, 2005; Gonzalez, Lerch & Lebiere, 2003). For example, when we want to collect information about a product, we first select a source (e.g., a store; the first random variable) and then get samples from this source (answers to questions; the second random variable). Similarly, when deciding between several garments (each placed in a separate rack in a store), we might first select a rack (first random variable) and then decide to get samples from the chosen rack (the second random variable). Up to now, research has paid little attention to the DE gap in gambles where the options differ in the number of random variables. In this paper, we set two explicit goals. First, we determine the degree of people’s aversion to ambiguity when people are presented simultaneously with the same option as either risky (one random variable) or ambiguous (more than one random variables) in a descriptive form. Second, we contrast this descriptive situation with a similar situation now presented in the sampling paradigm to determine people’s attitude to ambiguity in decisions from experience. Thus, we test whether the additional complexity in the ambiguous option results in ambiguity aversion in decisions from description and, more importantly, whether this additional complexity can lead to ambiguity-seeking in decisions from experience. In other words, is there a DE gap when people are asked to choose between a risky option and an ambiguous option, where the options differ on the number of random variables? DECISIONS UNDER RISKY AND AMBIGUOUS CONDITIONS In contrast to a risky option, in an ambiguous option, all possible values of probability (between 0 and 1) could be assumed to be equally likely, with the midpoint of the range of possible likelihoods (e.g., .5) as the best estimate (Weber & Johnson, 2008). However, Ellsberg (1961) showed that when presented with described risky and ambiguous options, people have a clear preference for the former rather than the latter—a behavior that Ellsberg called ambiguity aversion. Ambiguity aversion has been observed in both laboratory experiments and in real-world health, environmental, and negotiation contexts (Camerer & Weber, 1992; Curley & Yates, 1989; Hogarth & Kunreuther, 1989; Wakker, 2010). For example, Camerer and Weber (1992) provided a thorough review of the literature on decisions under ambiguity and showed that ambiguity aversion is a very stable phenomenon observed in a large number of described problems. Although ambiguity aversion prevails robustly for described gains, the case is less clear for described losses (Wakker, 2010). For losses, some researchers found ambiguity aversion behavior (Keren & Gerritsen, 1999), some found mixed evidence (Cohen, Jaffray & Said, 1987; Dobbs, 1991; Hogarth & Kunreuther, 1989; Mangelsdorff &Weber, 1994; Viscusi & Chesson, 1999), and a number of researchers found ambiguity-seeking behavior (Abdellaoui, Vossmann & Weber, 2005; Chakravarty & Roy, 2009; Davidovich & Yassour, 2009; Di Mauro & Maffioletti, 1996; Du & Budescu, 2005; Einhorn & Hogarth, 1986; Ho, Keller & Keltyka, 2002). Ambiguity aversion is a well-known phenomenon in decisions from description. However, very little is currently known about ambiguity aversion in situations involving experiential decisions. In fact, although the study of the DE gap has been prominent for risky decisions, the existence of a similar gap for a choice between risky and ambiguous decisions has yet to be investigated. Such research that shows a DE gap becomes important because some researchers have described experiential decisions under risk to be similar to decisions involving ambiguity (Fox & Hadar, 2006; Hadar & Fox, 2009). According to Hadar and Fox (2009), decisions from experience apply to any situation in which there is ambiguity and learning through trial-and-error feedback (i.e., sampling of outcomes). However, Hadar and Fox (2009) do not say anything about what it means to have an experiential counterpart to a given description in decisions under ambiguity, an assumption that is crucial to the equivalence of descriptive and experiential decisions and to the study of the DE gap in decisions under ambiguity. Arló-Costa and Helzner (2009) and Arló-Costa et al. (2011) have defined decisions from description and experience so that one could create equivalent experiential and descriptive counterparts for problems involving ambiguity. According to Arló-Costa et al. (2011), in risky options, people are presented with a specification of a chance mechanism, whereas in ambiguous options, people are not presented with such a specification; rather, they are allowed A random variable conceptually does not have a single, fixed value (even if unknown); rather, it can take on a set of possible different values, each with an associated probability. In this paper, the risky option has a single random variable; however, the ambiguous option has two random variables. DE Gap in Risky and Ambiguous Gambles 317 V. Dutt et al. Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 27, 316–327 (2014)