Reaction-Time Assessment of Beliefs Underlying the Irrational "Ratio-Bias" in Choice

Reaction-Time Assessment of Beliefs Underlying the Irrational Ratio-Bias in Choice. Kimihiko YAMAGISHI Yu NISHIMURA (kimihiko@ky.hum.titech.ac.jp) (yunishi@ky.hum.titech.ac.jp) Graduate School of Decision Science & Technology Tokyo Institute of Technology, Box W9-21 Ohokayama 2-12-1, Meguro-Ku, Tokyo 152-8552, JAPAN Abstract People often judge uncertainty expressions by ratios composed of greater numbers (e.g., 100 out of 5,000) as more probable than consisting of smaller ones (e.g., 1 out of 50). Literature refers to this well-replicated phenomenon as the ratio-bias. We investigated an irrational choice reflecting the ratio-bias, wherein decision makers preferred a 9/100 chance of winning a gamble over 1/10. Our analyses went beyond previous account of this irrationality by empirically assessing decision makers' subconscious belief pertaining to this choice situation. We found that decision makers exhibiting such preferences associated the 9/100 chance to benefits more strongly to 1/10. Therefore, they preferred the alternative which they unconsciously evaluated as more lucrative. We shall discuss implications for decision making literature supporting the dichotomy of cognitive systems into quick and irrational and slow, deliberate, and rational. Imagine yourself preparing for a business trip. The Federal Aviation Administration (FAA) has been practicing random screening of passengers at the airport. If this occurred to you, the security personnel would pull you out of line and check you more thoroughly, taking your time. Therefore you had better go to the airport well in advance to departure. How often would it occur? After searching the Internet, you find one webpage describing the possibility as 1 in 250, whereas another page showing 10 in 2,500. Now, which webpage suggests a greater chance of running into this drudgery? The rational answer, of course, is that both sources of information communicate exactly the same degree of uncertainty, namely 0.4%. However, people often perceive the latter representing a greater chance than the former. Literature shows numerous examples of this irrational belief affecting wide variety of judgment and choice, referring to this tendency as ratio-bias. McFarland and Miller (1994) told their participants that s/he ranked at the 30th percentile on a fictitious Social Perceptiveness Ability test. Concretely, the participants were told their rank as either 300th among 1,000 people or 3rd in 10. As the group size increased, pessimistic participants self-rated lower ability levels, whereas optimistic participants reported higher ability. In Miller, Turnbull and McFarland's (1989) vignettes, a child who adored chocolate-chip cookies successfully found such a cookie. Two vignettes differed in that the cookie jar contained chocolate-chip and less attractive oatmeal in the combination of either 1 and 19 or 10 and 190. The participants judged the child who succeeded in picking up 1 chocolate out of 20 as more suspicious of cheating, expressing their belief that a 1 in 20 chance was less likely to actualize than 10 in 200. Moreover, ratio-biases extended to cases of uneven odds. In risk perception, Yamagishi (1997) reported that people rated cancer as more seriously life-threatening when they read that cancer kills 1286 out of 10,000 people in the population than 24.14 out of 100. Perhaps the most straightforward example of irrationality due to the ratio-bias may be found in the experiment of Denes-Raj and Epstein (1994). Denes-Raj and Epstein presented participants with a pairwise choice of gambles. Option 1 offered a 1-out-of-10 chance (10%) of winning $1. Option 2 offered a 9-out-of-100 chance (9%) of winning the same amount. The majority of participants preferred Option 2 despite that Option 1 offered a superior percentage to win. In response to the experimenter's interview for justifications of the choice, the participants admitted the irrationality in their preference. In contrast, when the same participants faced another gamble situation with negative payoffs (i.e., the chance was to lose their money), the majority chose the option offering a smaller chance to lose, thereby performing rationally. The current investigation focuses exclusively on this phenomenon, and we refer to this study as the DRE experiment. We regard the ratio-bias instantiated by the DRE experiment, especially favoring a 9/100 chance to win over 1/10, as a striking example of irrationality for the following reasons. First, the irrationality is self-evident such that a naive person without formal training on rational theories of choice would easily comprehend why such preference is logically indefensible 1 . Second, despite the simplicity in the observed phenomenon per se, influential explanatory theories of decision making such as Prospect Theory (Kahneman & Tversky, 1977) fail to explain the DRE experimental result. Compare the DRE experimental finding to, for example, the oft- cited Allais paradox in decision making literature (Allais, 1953). It requires profound understanding of the normative desiderata of rational choice (e.g., von Neumann and Morgenstern (1944)) to appreciate why preference in the Allais paradox lacks logical coherence.