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Recognizing Ambiguity Re c o g n i z i n g Am b i g u i t y been offered as a decision tool by Daniel Ho w LA c k o f in f o R m A t i o n Sc ar e S uS Goldstein and Gerd Gigerenzer under an alternate approach to decision theory called Mark Clements “bounded rationality.”2 The purpose of Columbia University this exercise is to examine how each of these approaches accounts for decision behavior when faced with the same decision problem. In doing so, we will be able to determine I. Abstract how relevant these competing theories are In this paper, I will examine two to each other and discover the limitations different approaches to an experimental of the heuristic approach in pursuing a decision problem posed by Craig Fox and comprehensive model for rational decision Amos Tversky. This decision problem is making. intended to illustrate the phenomenon called “ambiguity aversion” that is observed II. Framework and Hypothesis in decision situations under uncertainty. Before proceeding, we need to establish These situations occur when an agent is the framework for the hypothesis that is faced with a decision problem where the under question here. Fox and Tversky are probabilities are not specified in advance attempting to identify decision situations or readily assessed based on the given where agents exhibit ambiguity aversion. information in the decision problem. They claim that comparative ignorance Because ambiguity aversion in decisions effects cause ambiguity aversion and that under uncertainty is one of the most this is an instance of preference reversal.3 fundamental problems of traditional Fox and Tversky don’t attempt to solve the decision theory1, in attempting to give problem of preference reversal; rather, they an account of rational decision making pose a hypothesis to describe the decision Fox and Tversky offer a hypothesis to situations where ambiguity aversion account for ambiguity aversion and manifests. They successfully support explain the decision situations that exhibit their hypothesis in experimental decision this problem. After examining their situations by restricting ambiguity aversion explanation for ambiguity aversion, I will to situations where comparative ignorance consider another possible approach to exists. However, this only identifies the these decision problems under uncertainty viz. the recognition heuristic, which has 2 Simon, 1955 3 It’s debatable if prefrence reversal is confined to 1 By “traditional decision theory” I mean subjective comparative ignorance and ambiguity aversion, but this expected utility maximization. seems to be the approach taken by Fox and Tversky. 24 domain of relevance for ambiguity aversion which would be devoid of the problematic while ignoring the more general problem axioms and utility maximization demanded of preference reversal in traditional in the traditional theory for explaining decision theory. such decision problems under uncertainty. This reversal of preferences is one of I will attempt to apply the recognition the major problems faced by traditional heuristic to Fox and Tversky’s experimental expected utility theory. It is observed in the decision problem to see if it is able to Ellsberg problem, where agents systemically give the same decision outcomes. If this violate one of the basic axioms of subjective application is successful in this case, then expected utility theory: Savage’s “sure there might be good reason for using this thing principle,” or the “independence” heuristic to supplement the traditional axiom. I’m not going to digress into an decision theory in situations under explanation of this problem because it is a uncertainty that illicit irrational choice prominent issue in the literature, so prior behavior due to axiom violation. If this familiarity with the issues posed by Ellsberg attempt is not successful, then the relevance will be assumed here. Essentially, Fox and and usefulness of such heuristics in a Tversky claim that the preference reversal comprehensive model for decision making is attributed to ambiguity aversion under must be examined. comparative ignorance. Because Fox and Tversky fail to III. Fox and Tversky – Ambiguity Aversion address the broader difficulties posed I will begin my analysis by examining by ambiguity aversion, we might wonder Fox and Tversky’s experimental setup if the recognition heuristic of bounded and the decision problem that is being rationality proposed by Goldstein and observed. As stated above, they propose Gigerenzer could resolve this problem. If a hypothesis to account for decision so, how would it resolve the problem? If situations that exhibit ambiguity aversion. the heuristic model proposed by Goldstein This is their “comparative ignorance and Gigerenzer can be applied to Fox and hypothesis”, which states “ambiguity Tversky’s decision experiment and develop aversion will be present when subjects 4 the same empirical trends , then decision evaluate clear and vague prospects jointly, patterns that exhibit preference reversal but it will greatly diminish or disappear can be accounted for in a theory of rational when they evaluate each prospect in decision making. The recognition heuristic isolation.”5 This is the hypothesis they would provide an alternative method, are testing in their experiment, which presents people with the following decision 4 That is, the heuristic will also instruct agents to choose the clear bet, which is the decision exhibited in Fox and Tversky’s experiment. 5 Fox and Tversky, 588 25 problem: situation with one evaluating the clear bet Imagine that there is a bag on the table alone, and the other, the vague bet alone. (Bag A) filled with exactly 50 red poker The results of their experiment show that in chips and 50 black poker chips, and a the comparative group, people priced the second bag (Bag B) filled with 100 poker clear bet significantly higher than the vague chips that are red and black, but you do not bet; in the non-comparative groups, there know their relative proportion. Suppose wasn’t a significant price difference between 7 that you are offered a ticket to a game that these two bets. The decision pattern is to be played as follows: First, you are to exhibited in this experiment supports their guess a color (red or black). Next, without hypothesis that in decision situations of looking, you are to draw a poker chip out of comparative ignorance, ambiguity aversion one of the bags. If the color that you draw is exhibited by people preferring the clear 8 is the same as the one you predicted, bet to the vague bet. then you will win $100; otherwise you win In verifying their hypothesis, Fox nothing. What is the most you would pay and Tversky conclude that comparative for a ticket to play such a game for each of situations between one clear option the bags? ($0-$100) and one vague option exhibit ambiguity aversion, and that this accounts for pref- Bag A Bag B erence reversal in cases such as Ellsberg’s problem.9 They further conclude that 50 Red Chips ? Red Chips traditional decision theory “requires that 50 Black Chips ? Black Chips the comparative and non-comparative 100 Total Chips 100 Total Chips evaluations will coincide” (by virtue of the independence axiom), but it does The most I would be willing to pay for a not “provide a method for reconciling ticket to Bag A (50 red; 50 black) is:___ inconsistent preferences.”10 By successfully The most I would be willing to pay for a identifying choice situations of comparative ticket to Bag B (? red; ? black) is:_____6 ignorance as exhibiting ambiguity aversion, their results are beneficial to traditional Fox and Tversky conducted this decision theory because they restrict the experiment with three groups of people. domain of relevance of the preference The first group evaluated the clear and vague bets in a comparative situation 7 Ibid., 589 as shown above. The other two groups 8 Preference in the sense that they were willing to wager more on the clear bet over the vague bet. They go on evaluated the bets in a non-comparative to conduct several other experiments that show similar results in support of this hypothesis. 9 Ibid., 600 6 Ibid. 10 Ibid. 26 reversal problem to decision situations of novel and the previously experienced.11 this type. Although this identification is Simply put, “recognized objects” are valuable for traditional decision theory, objects we’ve experienced before and it doesn’t solve the fundamental problem “unrecognized objects” are novel objects. illustrated by Ellsberg. Could bounded With this understanding of ‘recognition,’ rationality’s alternative approach to Goldstein and Gigerenzer explore the decision making provide a solution to this mechanics of the heuristic by asking problem? Possibly, but we would have an individual to consider the decision to determine which tool in the “adaptive problem of “inferring which of two objects toolbox” is appropriate to use in this has a higher value on some criterion.”12 situation. Now that the decision problem In evaluating this decision problem, the of Fox and Tversky has been identified recognition heuristic says that “if one of I will define the recognition heuristic as two objects is recognized and the other is described by Goldstein and Gigerenzer, not, then infer that the recognized object provide a justification for attempting to has the higher value.”13 apply it here, and then see if it is, in fact, Goldstein and Gigerenzer applicable in this case. demonstrate the use of their heuristic in an experiment involving German IV. The Recognition Heuristic and American students deciding which In the book Simple Heuristics that particular American city has the higher Make Us Smart, Daniel Goldstein and population. In their example, the two Gerd Gigerenzer outline a simple heuristic objects are San Diego and San Antonio, that describes decision patterns under a and the criterion is population.
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