Dual process in large number estimation under uncertainty

Dual process in large number estimation under uncertainty Miki Matsumuro (muro@cog.human.nagoya-u.ac.jp) Kazuhisa Miwa (miwa@is.nagoya-u.ac.jp) Hitoshi Terai (terai@is.nagoya-u.ac.jp) Kento Yamada (yamada@cog.human.nagoya-u.ac.jp) Graduate School of Information Science, Nagoya Univerasity, Fro-cho, Chikusa-ku, Nagoya, Japan Abstract According to the dual process theory, there are two systems in the mind: an intuitive and automatic System 1 and a logical and effortful System 2. This study focused on the System 2 process for large number estimation. First, we constructed a process model of estimation. The model, corresponding to the problem-solving process, consisted of creating subgoals (Sys- tem 2), retrieving values (System 1), and applying operations (System 2). Additionally, a knowledge network was used for the estimation process. Second, the results of an experiment based on our model showed that the deliberative System 2 pro- cess did not improve the value estimated by the intuitive Sys- tem 1 process. Keywords: Dual process theory, large number estimation, rea- soning, problem solving, knowledge network. Introduction How many piano tuners are there in the world? This is a well-known problem from a Google entrance ex- amination. The question is a type of a Fermi problem that re- quires the estimation of a quantity that is difficult to measure directly. The estimation needs to be conducted on the basis of uncertain and limited information. In this study, we call this type of estimation “estimation under uncertainty.” Many pre- vious studies have investigated intuitive aspects and heuristics of this estimation. However, when tackling the Google prob- lem, one tries to reach the correct answer systematically. In this study, we investigated a logical and deliberative process and its capability to estimate under certainty. Evans (2003) and Kahneman (2011) argued that there are two systems in the mind: System 1 and System 2. System 1– also called the heuristic process–operates automatically and quickly, with little or no effort, and no sense of voluntary control. However its judgments and estimations are intuitive and biased. It selects and retrieves relevant information au- tomatically. System 2 conducts a conscious and deliberate process in which a person approaches a goal step by step. Al- though the operations of System 2 are effortful and slow, they are rational and logical. In this study, we focus on the role of System 2 in estimation under uncertainty. Tversky and Kahneman (1974)’s review of heuristics and biases in judgment under uncertainty is one of the most fa- mous previous studies. They introduced three heuristics, cited in many studies of estimation: representativeness, avail- ability, and anchoring (originally adjustment and anchoring). We estimate likelihood, frequency, or quantity based on rep- resentativeness of an instance or availability of information. For example, Brown and Siegler (1992) showed that, when estimating the population of 99 countries, the more knowl- edge that participants had about a country, the larger they es- timated its population to be. System 1 uses such information unconsciously. The anchoring effect implies a tendency to rely too heav- ily on prior information (the anchor). Kahneman (2011) discussed that two different mechanisms produced this ef- fect, one for each system. First is selective accessibility. When System 1 assesses an anchor value, the accessibility of anchor-consistent information is selectively increased, which biases the judgment. Strack and Mussweiler (1997) showed that even an implausible anchor value produced an anchoring effect. Second, Tversky and Kahneman (1974) originally sug- gested that a process of adjustment by System 2 produced the anchoring effect. Participants start estimating from an anchor value, assess whether it is too high or too low, and adjust it. An insufficient adjustment results in an estimated value biased toward the initial value. Epley and Gilovich (2001) demonstrated that the type of anchor value, whether self-generated or provided, affected which mechanism was dominant. Another factor, familiarity with a variable to be estimated, also affects the estimated value; estimation of a fa- miliar variable is easy and accurate (Block & Harper, 1991). As stated above, while many previous studies have focused on simple heuristics and automatic processes, the deliberative System 2 process has not been sufficiently studied. To investigate the process of estimation under uncertainty, we assume that it represents a kind of problem solving. We focus on means-ends analysis, a problem-solving strategy (Newell & Simon, 1972). Given a current state and a goal state, an operation that will reduce the difference between the two states is applied to the current state. When a goal is not immediately attainable, we break the problem down into smaller problems by creating a subgoal. A similar pro- cess is expected in estimation under uncertainty. A goal state is one in which the value of a target variable is known. Sub- goals would be created because it is difficult to reach the goal state directly. Some operations for estimating values would be observed. The first purpose of this study was to construct a process model of estimation under certainty, including the delibera- tive process of System 2. The second purpose was to inves- tigate whether a value estimated by the System 1 process is improved by the System 2 process. This investigation is im- portant because a value estimated by the System 1 process is susceptible to bias.