Cognitive Illusions

Intriguing Phenomena in Thinking, Judgment, and Memory

Rüdiger F Pohl

• Publisher: Routledge
• Year: 2022
• Print ISBN: 9780367724245
• eBook ISBN: 9781000548150
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Cognitive Illusions explores a wide range of fascinating psychological effects in the way we think, judge and remember in our everyday lives. In this volume, Rüdiger F. Pohl brings together leading international researchers to define what cognitive illusions are and discuss their theoretical status: are such illusions proof of a faulty human information-processing system, or do they only represent by-products of otherwise adaptive cognitive mechanisms?

The book describes and discusses 26 different cognitive illusions, with each chapter giving a profound overview of the respective empirical research including potential explanations, individual differences, and relevant applied perspectives. This edition has been thoroughly updated throughout, featuring new chapters on negativity bias, metacognition, and how we respond to fake news, along with detailed descriptions of experiments that can be used as classroom demonstration in every chapter.

Demonstrating just how diverse cognitive illusions can be, it is a must read for all students and researchers of cognitive illusions, specifically, those focusing on thinking, reasoning, decision-making, and memory.

Part I Thinking

doi: 10.4324/9781003154730-3

2 Conjunction fallacy

John E. Fisk

DOI: 10.4324/9781003154730-4

Violations of the rules of probability theory and associated systematic reasoning biases have been widely demonstrated. One area that has received much attention in the research literature concerns conjunction-rule violations. Formally, the conjunction rule may be expressed as follows:

P(A&B) = P(A) × P(B|A) (2.1)

Thus, the probability of event A and event B both occurring together is equal to the probability of event A multiplied by the (conditional) probability of event B given that A has occurred. For example, the probability that I will study (event A) AND pass my exams (event B) is equal to the probability that I will study multiplied by the probability that I will pass given that I have studied:

P(Study and Pass) = P(Study) × P(Pass | Study) (2.2)

When the two events A and B are independent then Equation 2.1 simplifies to

P(A&B) = P(A) × P(B) (2.3)

since for independent events:

P(B) = P(B|A) = P(B|not A) (2.4)

The extent to which individuals make judgments consistent with the conjunction rule has been one of the most investigated areas of probabilistic reasoning with research dating back over 50 years (e.g., Cohen et al., 1958). In the 1980s, starting with Tversky and Kahneman’s (1983) seminal study, the focus of research shifted to a particular type of violation of the conjunction rule known as the conjunction fallacy (Agnoli & Krantz, 1989; Fiedler, 1988; Wells, 1985; Yates & Carlson, 1986). Looking at Equation 2.1, P(A&B) ≤ P(A) since, by definition, P(B|A) ≤ 1 and by extension, it follows that P(A&B) ≤ (P(B). Thus the fallacy occurs when the conjunctive probability is assigned a value exceeding that assigned to one or both of the component events, that is,

P(A&B) > P(A) and/or (2.5)

P(A&B) > P(B), (2.6)

Perhaps the best-known example of the conjunction fallacy is the Linda scenario from Tversky and Kahneman’s (1983) classic study. In this scenario, a fictitious person, Linda, is described as follows:

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

Having read the description, individuals were asked to rank the following three statements in order of their probability:

Linda is active in the feminist movement.

Linda is a bank teller.

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

Clearly, the third statement is a conjunction of the first two and so according to the conjunction rule cannot be more likely than first and second statements. However, in Tversky and Kahneman’s (1983) study, 85% of participants committed the fallacy, ranking the third statement as more probable than the second. Since then and continuing up to the present day, numerous studies have produced evidence of the conjunction fallacy (e.g., Agnoli & Krantz, 1989; Costello & Watts, 2014; Fisk & Pidgeon, 1996; Hertwig & Chase, 1998; Nilsson et al., 2009; Rogers et al., 2011; Tentori et al., 2013; Yates & Carlson, 1986).

It is important to note that the fallacy is most common in cases where the conjunction contains a likely event (e.g., feminist) paired with an unlikely event (e.g., bank teller). In other contexts, the fallacy is much reduced, for example, where the conjunction contains two unlikely events (Fisk & Pidgeon, 1996; Wells, 1985). Details for a classroom demonstration are given in Text box 2.1.

Text box 2.1 Classroom demonstration

Background

Aczel et al. (2016) presented participants with a conjunction paired with either the more likely or the less likely component. They found that the value assigned to the conjunctive probability was substantially larger in the former case compared with the latter. Thus, it appeared that the probability assigned to the conjunctive event depended on which single event it was paired with, an outcome which, to the best of my knowledge, has not been previously observed. The following classroom demonstration seeks to replicate and extend this finding.

Method

The context within which the conjunctive probability is presented constitutes the independent variable with three levels: with the less likely component, with the more likely component, and with an unrelated statement. The dependent variable is the estimated value of the conjunction. Participants will be randomly assigned to three groups with each group receiving one of the following three versions of the Linda problem. All three versions start with Linda’s description (see above).

Participants are then asked: How likely are each of the following statements (for each, enter a percentage probability between 0 and 100):

Version 1 continues with the two following statements:

• Linda is a feminist.
• Linda is a bank teller and a feminist.

Version 2 continues with the two following statements:

• Linda is a bank teller.
• Linda is a bank teller and a feminist.

Version 3 continues with the two following statements:

• Linda is a socialist.
• Linda is a bank teller and a feminist.

The resulting three sets of conjunctive estimates can be analysed using one-way between participant ANOVA. The prediction is that the conjunctive estimate paired with the more likely component (Version 1) will be significantly larger than that paired with the less likely component (Version 2). While no prediction is made in relation to the conjunctive estimate from the third version, as will be clear having read the remainder of this chapter, I expect that it will be close in magnitude to the outcome for Version 2. Paired comparisons can be made using Tukey’s test. The incidence of the conjunction fallacy can be compared between Versions 1 and 2 using chi squared analysis. Fallacies are predicted to be rare in Version 1 and commonplace in Version 2.

Over the years, there has been doubt expressed as to whether the fallacy is a real phenomenon or the product of invalid experimental approaches. By way of contrast, the dominant view is that it represents a significant violation of normative reasoning. More recently, while accepting that the fallacy is a genuine phenomenon, its real-world significance has been questioned. I shall now examine each of these perspectives in turn.

Is the conjunction fallacy real?

The first question that must be addressed is whether the conjunction fallacy is a genuine phenomenon at all. Several researchers have suggested that what appears to be a reasoning error can be viewed as perfectly rational when viewed from an alternative perspective. We shall examine these differing explanations in the remainder of this section.

The laws of probability do not apply where there is subjective uncertainty

Maguire et al. (2018) have drawn a distinction between subjective and objective uncertainty. Objective uncertainty, they argued, is characterized by pure randomness where each event is independent and unconnected to any subsequent event (e.g., where the outcome probabilities are known a priori such as with the toss of a coin or the throw of a die). With subjective uncertainty, Maguire et al. maintained that events are not usually independent and may convey additional information as to the nature of the generative mechanism. In their view, potential events confronting the individual as part of their everyday lives are characterized by subjective uncertainty and rather than being viewed as straightforward possibilities they may be perceived as subjectively informative conveying some deeper meaning. As such, in considering the broader context suggested by the event in question, the individual may amend their understanding of the underlying situation going beyond the basic information provided. In the context of the conjunction fallacy, given the existence of subjective uncertainty, since Linda’s description (see above) is based on those attributes chosen by the experimenter, according to the Maguire et al. argument, the participant may view it as incomplete and partial. Equally, the statements to be considered may be viewed as potentially informative. In this context, given the individual’s evolving state of knowledge, the resulting conjunction may seem less surprising and subjectively more likely than the bank teller component statement on its own. Crucially, Maguire et al. maintained that this was not a fallacy since objective probabilities cannot be defined for the events in question which reflect the evolving state of knowledge concerning Linda.

According to Maguire et al., it is possible to change a problem from one involving subjective uncertainty to one involving objective uncertainty in which the rules of probability would apply. They produced a modified version of the Linda problem in which the participant was told that a social media database was searched by inputting the following randomly selected parameters:

• university degree = philosophy
• marital status = single
• IQ > 130
• name = Linda
• age = 31

The participant was informed that this returned a single database record and was asked which was more probable:

1. That the record states:

occupation = bank teller and political outlook = feminist

Or (2) that the record states:

occupation = bank teller

Maguire et al. found that the incidence of the conjunction fallacy was significantly reduced from 64% in the original version of the problem to 39% in the social media version. Nonetheless the fact that the incidence of the fallacy remained close to 40% is noteworthy.

Conversational implicature

Research questioning the veracity of the conjunction fallacy emerged shortly after the phenomenon was popularized by Tversky and Kahneman (1983). One strand of the research literature focused on the notion of conversational implicature – that is to say, where a communication has a meaning going beyond its literal interpretation. For example, when examining a p...

Table of contents

• Cover
• Half-Title Page
• Title Page
• Copyright Page
• Table of Contents
• List of Contributors
• Introduction
• Part I Thinking
• Part II Judgment
• Part III Memory
• Author Index
• Subject Index