Philosophy of Psychology. Lisa Bortolotti

Figure 1. Wason selection task with abstract options

Conjunction Fallacy

The next study involves the so-called ‘conjunction fallacy’ (also known as the conjunction effect), which is a mistake people make when they assume that a statement describing the conjunction of two states of affairs (e.g., ‘Tomorrow it will be raining and it will be cold’) is more probable than a statement describing one of those states of affairs alone (e.g., ‘Tomorrow it will be raining’).

      In one experiment by Tversky and Kahneman (1983), participants first read personality sketches of hypothetical people, and then answered questions about them. Participants were divided into three groups according to their background in probability and statistics: the naïve group (those with no background), the intermediate group (those with basic knowledge of probability and statistics), and the sophisticated group (those with advanced knowledge of probability and statistics). Here is the personality sketch of a hypothetical person, Linda.

      Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and participated in anti-nuclear demonstrations.

      Please rank the following statements by their probability, using 1 for the most probable and 8 for the least probable:

      1. Linda is a teacher in elementary school.

      2. Linda works in a bookstore and takes Yoga classes.

      3. Linda is active in the feminist movement.

      4. Linda is a psychiatric social worker.

      5. Linda is a member of the League of Women Voters.

      6. Linda is a bank teller.

      7. Linda is an insurance salesperson.

      8. Linda is a bank teller and is active in the feminist movement.

The result revealed that statements 3 and 7 were regarded, respectively, as the most probable and the least probable, which is explained by the similarity of Linda’s personality sketch with the stereotypical image of someone politically active, and the dissimilarity between her personality sketch and the stereotypical image of an insurance salesperson. The crucial statements to consider in this experiment are 6 and 8. The mean rank of the former was lower than the mean rank of the latter, which means that Linda being a bank teller and active in the feminist movement was regarded as more probable than her being a bank teller. This, however, is a mistake. Linda being a bank teller and active in the feminist movement is the conjunction of her being a bank teller and of her being active in the feminist movement. And the conjunction cannot be more probable than one of the conjuncts. Thus, this mistake is an obvious violation of the conjunction rule. This fallacy was found in all three groups of participants and background knowledge in statistics and probability did not have a significant effect on the participant’s performance.

Base-Rate Neglect

      In another famous experiment by Kahneman and Tversky (1973), half of the participants read a story, ‘cover story’, which said that psychologists prepared 100 personality descriptions on the basis of interviewing and testing 30 engineers and 70 lawyers. The other half of the participants read almost the same cover story, except that the number of engineers and the number of lawyers were switched; 70 engineers and 30 lawyers. Then participants were presented with personality descriptions – supposedly randomly selected from the 100 personality descriptions – and were asked to judge the probability of that person being an engineer. Here is one such description:

      Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles.

      One finding was that participants made a judgment on the basis of the stereotypes associated with the two occupations – engineer and lawyer – which is consistent with what we saw in the Linda experiment. Linda was regarded as most likely to be active in the feminist movement, which nicely fits the stereotype provided in her personal description. Similarly, in this study, Jack was most likely judged to be an engineer rather than a lawyer because his personality description nicely fits the stereotype of engineers. The crucial finding was that the base-rate information was largely neglected; the judgment was independent of the base rates provided in the cover stories.

This error constitutes a violation of Bayes’ rule, which says that the probability of an hypothesis H given an observation O (‘posterior probability’, P(H/O)) is determined by both how likely O is if H is true (‘likelihood’, P(O/H)), and how probable H is without the observation (‘prior probability’, P(H)). For example, the probability of Jack being an engineer given the personality description is determined by both how likely the personal description (being generally conservative, careful, ambitious, etc.) is if Jack is really an engineer, and how probable it is that Jack is an engineer without the personal description. What happened in the experimental results was that the participants largely ignored the prior probability (i.e., how probable it is that Jack is an engineer without the personal description) which is determined by the base-rate. Thus, Kahneman and Tversky summarize their finding as follows:

      One of the basic principles of statistical prediction is that prior probability, which summarizes what we knew about the problem before receiving independent specific evidence, remains relevant even after such evidence is obtained. Bayes’ rule translates this qualitative principle into a multiplicative relation between prior odds and the likelihood ratio. Our subjects, however, fail to integrate prior probability with specific evidence. […] The failure to appreciate the relevance of prior probability in the presence of specific evidence is perhaps one of the most significant departures of intuition from the normative theory of prediction. (Kahneman & Tversky 1973, 243)

Preference Reversal

      Another area of weakness in human reasoning can be found in the psychology and economics literature on preference reversals. The principle of procedure invariance tells us that, given two options, if one prefers A to B, then this preference should not change when the method for eliciting the preference changes. Yet participants often state a preference for A over B when they are asked to make a direct choice, but are prepared to pay more to obtain B than they are to obtain A.

Take two lotteries: a relatively safe lottery, where one has a 10% chance of winning nothing and a 90% chance of winning £10; and a relatively risky lottery, where one has a 10% chance of winning £90 and a 90% chance of winning nothing. If asked to choose, people usually prefer to buy a ticket for the safer lottery. In contrast, if asked at what price they would sell their ticket, they set a higher selling price for the ticket of the risky lottery. This phenomenon is observed in different contexts of choice and matching too (Stalmeier, Wakker, & Bezembinder 1997).

      The classic example of the violation of procedure invariance in the literature is the Traffic Problem (Tversky & Thaler 1990, 201–202):

      (1) The Minister of Transportation is considering which of the following two programs would make the electorate happier:

      Program A is expected to reduce the yearly number of casualties in traffic accidents to 570 and its annual cost is estimated at $12 million.

      Program B is expected to reduce the yearly number of casualties in traffic accidents to 500 and its annual cost is estimated at $55 million.

      Which program would you like better?

      (2) The Minister