Academic journal article Psychonomic Bulletin & Review

Bats, Balls, and Substitution Sensitivity: Cognitive Misers Are No Happy Fools

Academic journal article Psychonomic Bulletin & Review

Bats, Balls, and Substitution Sensitivity: Cognitive Misers Are No Happy Fools

Article excerpt

Published online: 16 February 2013

© Psychonomic Society, Inc. 2013

Abstract Influential work on human thinking suggests that our judgment is often biased because we minimize cognitive effort and intuitively substitute hard questions by easier ones. A key question is whether or not people realize that they are doing this and notice their mistake. Here, we test this claim with one of the most publicized examples of the substitution bias, the bat-and-ball problem. We designed an isomorphic control version in which reasoners experience no intuitive pull to substitute. Results show that people are less confident in their substituted, erroneous bat-and-ball answer than in their answer on the control version that does not give rise to the substitution. Contrary to popular belief, this basic finding indicates that biased reasoners are not completely oblivious to the substitution and sense that their answer is questionable. This calls into question the characterization of the human reasoner as a happy fool who blindly answers erroneous questions without realizing it.

Keywords Judgment and decision making . Decision making

Human reasoners have been characterized as cognitive misers who show a strong tendency to rely on fast, intuitive processing rather than on more demanding, deliberate thinking (Evans, 2008;Kahneman, 2011). Although the fast and effortless nature of intuitive processing can sometimes be useful, it can also bias our reasoning. It has been argued that the key to this bias is a process of so-called attribute substitution: When people are confronted with a difficult question, they often intuitively answer an easier one instead (e.g., Kahneman, 2011; Kahneman & Frederick, 2002). Consider the following example:

A bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

When you try to answer this problem, the intuitive answer that immediately springs to mind is "10 cents." Indeed, about 80 % of university students who are asked to solve the bat-and-ball problem give the "10 cents" answer (e.g., Bourgeois-Gironde & Vanderhenst, 2009). But it is wrong. Obviously, if the ball were to cost 10 cents, the bat would cost $1.10 (i.e., $1 more), and then the total cost would be $1.20, rather than the required $1.10. The correct response is "5 cents," of course (i.e., the bat costs $1.05). The explanation for the widespread "10 cents" bias in terms of attribute substitution is that people substitute the critical relational "more than" statement by a simpler absolute statement. That is, "the bat costs $1 more than the ball" is read as "the bat costs $1." Hence, rather than working out the sum, people naturally parse $1.10, into $1 and 10 cents, which is easier to do. In other words, because of the substitution, people give the correct answer to the wrong question.

The bat-and-ball problem is considered a paradigmatic example of people's cognitive miserliness (e.g., Bourgeois- Gironde & Vanderhenst, 2009; Kahneman, 2011; Kahneman & Frederick, 2002; Toplak,West,&Stanovich, 2011). After all, the problem is really not that hard. Clearly, if people reflected upon it for even a moment, they would surely realize their error and notice that a 10 cents ball and a bat that costs a dollar more cannot total to $1.10. Hence, the problem with attribute substitution seems to be that people typically do not notice that they are substituting and do not realize their error (Kahneman & Frederick, 2005; Thompson, 2009; Toplak et al., 2011). This can sketch a somewhat bleak picture of human rationality: Not only do we often fail to reason correctly, much like happy fools, we do not even seem to realize that we are making a mistake.

However, the fact that decision-makers do not deliberately reflect upon their response does not necessarily imply that they are not detecting the substitution process. That is, although people might not engage in deliberate processing and might not know what the correct answer is, it is still possible that they have some minimal substitution sensitivity and at least notice that their substituted "10 cents" response is not completely warranted. …

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