Effects of Problem Schema on Successful Maximizing in Repeated Choices

Effects of Problem Schema on Successful Maximizing in Repeated Choices Jie Gao (jg2902@columbia.edu) Center for Decision Sciences, Columbia University New York, NY 10027 USA James E. Corter (jec34@columbia.edu) Teachers College, Columbia University New York, NY 10027 USA Regarding statistical concepts, Nisbett, Krantz, Jepson, and Kunda (1983) argue that people learn intuitive versions of abstract principles such as the law of large numbers through life experience in various domains. These representations are often referred to as statistical heuristics. These heuristics can be improved by statistical training and successfully applied across domains (Fong, Krantz & Nisbett, 1986). Nonetheless, people do not always use statistical reasoning when it is appropriate (e.g., Tversky & Kahneman, 1974). Accordingly, Nisbett et al. argue that it is important to study what kinds of events and problems most often elicit statistical reasoning. They list three factors that affect whether statistical reasoning is applied in a particular context: the clarity of the sample space and the sampling process, the perceived relevance of chance factors, and cultural norms for the specific domain. We believe that such pragmatic or semantic factors can affect learning and application of formal knowledge across a broad array of tasks, including optimal versus non-optimal choices in decision making. Thus, in the present paper we investigate the influence of such prior pragmatic knowledge on people’s ability to find and select the “rational” or optimal strategy in repeated random binary choices, a situation where sub-optimal behavior (specifically, probability matching) is not infrequent. To illustrate, imagine Situation 1, wherein a die with two faces colored black and four colored red is rolled, and suppose that your task is to predict the color that will occur on each of the next five rolls. Now imagine Situation 2, where there are two dice, the first colored as above and the second with the colors reversed. Here, your task is to predict which die will show red, on each of five successive trials. Although the two situations share many surface features (and the same objective probability of success on each trial, if you pick the more likely outcome), we believe that they are psychologically different, that they are associated with different experience-based pragmatic schema. In the first example, the two possible outcomes, black and red, are not just negatively correlated, they are complementary events. In terms of experience, this situation may be associated with common everyday examples of repeatedly trying to predict a binary outcome: Heads versus Tails, making a shot in basketball versus missing it, will it be a sunny day or a rainy day? In most of these experienced situations, the element of chance variation is very salient. Abstract We investigate the effects of problem schema type (complementary events versus independent events) on participants’ tendency to adopt probability matching or maximizing strategies across repeated decisions. These two general problem types were compared in an online study (N=300), using a between-subjects design. We also varied abstraction level of the problem story context, using abstract contexts, contexts involving physical randomizing devices, and “real-world” social/pragmatic contexts. Participants made a binary choice on each of 20 trials, receiving trial-by-trial outcome feedback. Maximization was consistently higher for independent events contexts than for complementary, while abstraction level of the context had no significant effect on the prevalence of maximizing behavior. The results support our hypothesis that people may find it especially difficult to discover the maximizing strategy for problems exemplifying the complementary-outcomes schema. In contrast, when the problem involves choosing between two distinct objects or entities (a common instantiation of the independent events schema) it seems to be easier to maximize, perhaps due to cueing of a pragmatic “pick the winner” schema. Keywords: probability matching; maximizing; repeated decisions; pragmatic schemas; abstraction Introduction It has been shown that past experience has an important impact on people’s reasoning and decision making. In one influential line of research, Cheng and Holyoak (1985) argue that people often reason not according to the rules of formal logic, but based on a set of abstract (or partly abstract) knowledge structures induced from daily-life experience. They term these knowledge structures “pragmatic reasoning schemas”. These pragmatic schemas have been shown to affect people’s perceptions, problem solving and decision making. For example, many studies have shown that reasoning problems that are situated in a real-world context are solved more easily than those posed in purely abstract forms (Evans, 1982; Johnson-Laird et al., 1972; Wason, 1966; Wason & Evans, 1975). Other researchers have found a significant impact of previous life experience on perception and cognition, both experience in the physical world (Tooby & Cosmides, 1992) and in domains that are abstracted from or unrelated to the physical environment (cf. Bargh, 2006). Williams, Huang and Bargh (2009) have used the term “mind scaffolding” to refer to how higher mental processes are often grounded in early experience of the physical world.