Violations of Dominance

Violations of Dominance

The conjunction fallacy observed in the Linda problem is an example of a dominance violation in judgment: Linda must be at least as likely to be a bank teller as to be a feminist bank teller, but people believe the opposite. Insensitivity to extension (in this case, base-rate) effectively guarantees the existence of such dominance violations.

For another illustration, consider the question, “How many murders were there last year in [Detroit/Michigan]?” Although there cannot be more murders in Detroit than in Michigan because Michigan contains Detroit, the word Detroit evokes a more violent image than the word Michigan (except, of course, for people who immediately think of Detroit when Michigan is mentioned). If people use an impression of violence as a heuristic and neglect geographic extension, their estimates of murders in the city may exceed their estimates for the state. In a large sample of University of Arizona students, this hypothesis was confirmed – the median estimate of the number of murders was 200 for Detroit, and 100 for Michigan.

Violations of dominance akin to the conjunction fallacy have been observed in several other experiments, involving both indirect (between-subjects) and direct tests. In a clinical experiment reported by Redelmeier, Katz, and Kahneman (2001), half of a large group of patients (N = 682) undergoing a colonoscopy were randomly assigned to a condition that made the actual experience strictly worse. Unbeknownst to the patient, the physician deliberately delayed the removal of the colonoscope for approximately 1 minute beyond the normal time. For many patients, the mild discomfort of that extra period was an improvement relative to the pain that they had just experienced. For these patients, of course, prolonging the procedure reduced the Peak/End average of discomfort. As expected, retrospective evaluations were less negative in the experimental group. Remarkably, a 5-year follow-up showed that participants in that group were also somewhat more likely to comply with recommendations to undergo a repeat colonoscopy (Redelmeier, Katz, & Kahneman, 2001).

In an experiment that is directly analogous to the demonstrations of the conjunction fallacy, Kahneman et al. (1993) exposed participants to two cold-pressor experiences, one with each hand: a short episode (immersion of one hand in 14°C water for 60 seconds), and a long episode (the short episode plus an additional 30 seconds during which the water was gradually warmed to 15°C). The participants indicated the intensity of their pain throughout the experience. When they were later asked which of the two experiences they preferred to repeat, a substantial majority chose the long trial. These choices violate dominance, because after 60 seconds in cold water most people prefer the immediate experience of a warm towel to 30 extra seconds of slowly diminishing pain. In a replication, Schreiber and Kahneman (2000, Exp. 2) exposed participants to pairs of unpleasant noises in immediate succession. The participants listened to both sounds and chose one to be repeated at the end of the session. The short noise lasted 8 seconds at 77 db. The long noise consisted of the short noise plus an extra period (of up to 24 sec) at 66 db (less aversive, but still unpleasant and certainly worse than silence). Here again, the longer noise was preferred most of the time, and this unlikely preference persisted over a series of five choices.

The violations of dominance in these direct tests are particularly surprising because the situation is completely transparent. The participants in the experiments could easily retrieve the durations of the two experiences between which they had to choose, but the results suggest that they simply ignored duration. A simple explanation is that the results reflect “choosing by liking” (see Frederick, Chapter 30, this volume). The participants in the experiments simply followed the normal strategy of choice: “When choosing between two familiar options, consult your retrospective evaluations and choose the one that you like most (or dislike least).” Liking and disliking are products of System 1 that do not conform to the rules of extensional logic. System 2 could have intervened, but in these experiments, it generally did not. Kahneman et al. (1993) described a participant in their study who chose to repeat the long cold-pressor experience. Soon after the choice was recorded, the participant was asked which of the two experiences was longer. As he correctly identified the long trial, the participant was heard to mutter, “The choice I made doesn’t seem to make much sense.” Choosing by liking is a form of mindlessness (Langer, 1978) that illustrates the casual governance of System 2.

Like the demonstrations of the conjunction fallacy in direct tests (discussed earlier), violations of temporal monotonicity in choices should be viewed as an expendable flourish. Because the two aversive experiences occurred within a few minutes of each other, and because respondents could recall accurately the duration of the two events, System 2 had enough information to override choosing by liking. Its failure to do so is analogous to the failure of people to appreciate the set inclusion rule in direct tests of the conjunction fallacy. In both cases, the violations of dominance tell us nothing new about System 1; they only illustrate an unexpected weakness of System 2. Just as the theory of intuitive categorical prediction would have remained intact if the conjunction fallacy had not “worked” in a direct test, the model of evaluation by moments would have survived even if violations of dominance had been eliminated in highly transparent situations. The same methodological issues arise in both contexts. Between-subjects experiments or subtle tests are most appropriate for studying the basic intuitive evaluations of System 1, and also most likely to reveal complete extension neglect. Factorial designs in which extension is manipulated practically guarantee an effect of this variable, and almost guarantee that it will be additive, as in Figures 2.3B and 2.3D (Ariely, 1998; Ariely, Kahneman, & Loewenstein, 2000; Schreiber and Kahneman, 2000). Finally, although direct choices sometimes yield systematic violations of dominance, these violations can be avoided by manipulations that prompt System 2 to take control.

In our view, the similarity of the results obtained in diverse contexts is a compelling argument for a unified interpretation, and a significant challenge to critiques that pertain only to selected subsets of this body of evidence. A number of commentators have offered competing interpretations of base-rate neglect (Cosmides & Tooby, 1996; Koehler, 1996), insensitivity to scope in WTP (Kopp, 1992), and duration neglect (Ariely & Loewenstein, 2000). However, these interpretations are generally specific to a particular task and would not carry over to analogous findings in other domains. Similarly, the various attempts to explain the conjunction fallacy as an artifact do not explain analogous violations of dominance in the cold-pressor experiment. The account we offer is, in contrast, equally applicable to all three contexts and possibly others as well (see also Kahneman, Ritov, & Schkade, 1999). We attribute extension neglect and violations of dominance to a lazy System 2 and a prototype heuristic that combines two processes of System 1: the representation of categories by prototypes and the substitution of a nonextensional heuristic attribute for an extensional target attribute. We also propose that people have some appreciation of the role of extension in the various judgment tasks. Consequently, they incorporate extension in their judgments when their attention is drawn to this factor – most reliably in factorial experiments and sometimes (although not always) in direct tests. The challenge for competing interpretations is to provide a unified account of the diverse phenomena that have been considered in this section.