with confidence, observing the maxim of quality. But in context of an accompanying statement that. "Linda is a bank teller and is active in the feminist movement," ...
Conversation, Consciousness, and Conjunctions Dulany, D.E., & Hilton, D. (1991). Conversational implicature, conscious representation, and the conjunction fallacy. Social Cognition, 9, 85-110. Preprint Version:
Conversational Implicature, Conscious Representation and the Conjunction Fallacy Don E. Dulany University of Illinois at Urbana-Champaign Denis J. Hilton Zentrum für Unfragen, Methoden und Analysen, Mannheim Universitaet Mannheim
Abstract This study examined judgments in four of Tversky and Kahneman's (1983) conjunction tasks, applying Gricean principles of conversational implicature and an analysis of the subjects' conscious representations. Conversational inference is itself a form of judgment under uncertainty, and hearers often venture interpretations of a speaker's intention, constrained by assumptions embodying rules of conversation. For a conjunction effect to be a fallacy, we argue, subjects must interpret the key conjunct extensionally; fallacious reasoning consists of deficient mental operations on one's own mental contents. We therefore assessed interpretations of the conjunct with reports or induced them with elaborative information, distinguishing extensional interpretations from those that absolve the judgment of fallacy. In Experiment 1, subjects most often formed absolving interpretations of the conjunct where they were most likely to judge the conjunction more probable than the conjunct. In Experiment 2, the conjunct was most often given the absolving interpretation that evidence was insufficient for saying more. Experiment 3 elaborated these results with experimentally induced interpretations. In Experiment 4, reports of representativeness were strongly related to conjunction effects and to reports of non-extensional interpretations, and there was no evidence of conjunction fallacies. Over these experiments, we estimate the incidence of genuine conjunction fallacies as between none to 38%, in contrast with the 85% and 90% Tversky and Kahneman reported. On our interpretation, the representativeness heuristic and conversational assumptions together work predominantly to frame conscious representations of the conjunct that absolve the conjunction effect of fallacy. Tversky and Kahneman (1982, 1983) have presented unusually provocative evidence that lay judgments of probability systematically violate the conjunction rule, a rule expressing the "simplest and most fundamental qualitative law of probability" (1983, p. 294). By that law, if B is included in the extension of A, the probability of B cannot exceed the probability of A. And according to the conjunction
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rule it implies, the probability that A&B both occur cannot Conversation, be greaterConsciousness, than the probability and Conjunctions that one of its constituents occurs: P(A&B) < P(B). This is simply because A is formally equivalent to ([A&B] or [A¬B]), and thus A&B is included within the possibility set of A, its extension. Nevertheless, it is their repeated finding that an impressive majority of subjects rate the conjunction more probable than one of its constituents, judgments they characterize as flagrantly in violation of the conjunction rule. In their best-known example, Tversky and Kahneman (1983) gave subjects a description of a woman who appears to be a social activist: 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 also participated in anti-nuclear demonstrations. In the so-called "direct transparent" version of the task, subjects were then asked to check which of the following two alternatives was more probable: Linda is a bank teller. (T) Linda is a bank teller and is active in the feminist movement. (T&F) In this version of the task, 85% of the subjects rated the conjunction (T&F) as being more probable than the single constituent (T)--evidently violating the conjunction rule. Indeed, with this and similar tasks, closely comparable proportions of subjects judged the conjunction more probable in "indirect tests," in which different subjects evaluated each assertion, and in "direct subtle tests," in which the same subjects rank ordered the probabili- ties of asserted events in a list including the conjunct and conjunction. In either of the two kinds of direct tests, judging the conjunction more probable than the conjunct is what Tversky and Kahneman (1983, p. 298) termed the conjunction fallacy. We shall, however, use the more neutral term "conjunction effect" to label that judgment and discuss the conditions under which it may and may not be a fallacy (cf. Leddo, Abelson, & Gross, 1984). On Tversky and Kahneman's view (1983, p. 294), these judgments, like many others, are unconstrained by extensional reasoning and follow instead from "natural assessments," in particular the heuristic of representativeness. This in turn is an assessment of the resemblance of samples, instances, or acts to populations, categories, or actors. Linda the teller and feminist, for example, seems more representative of collegiate activists than would Linda the plain teller. And in another of their scenarios, Mr. F at 50-something seems more representative of coronary victims than would just plain Mr. F. A heuristic, as Tversky and Kahneman see it, relies on natural assessments that are routine ways of perceiving events and understanding messages. They compare a conceptual fallacy to a perceptual illusion. This account has been remarkable for the inclination it produces to agree that the conjunction rule is incontestable, but to argue nevertheless that the conjunction effect may not be a fallacy after all-that the illusion may be less in the eyes of their subjects than in the eyes of their readers. If the subjects were only aware that "teller" is supposed to mean "teller and feminist or non-feminist," the thinking goes, then of course they would choose "teller;" so it must mean something else to them. The underlying issue, of course, is that of the senses and limits of rationality, the deeper concern that animates this and a number of related literatures (Cohen, 1981; Dawes, 1988; Johnson-Laird, 1983; Kruglanski, 1989). Adler (1984), for example, argues that it is anomalous to ask subjects to judge the relative probability of an item being a member of a set or its superset, just as in Piagetian experiments it is anomalous to ask a child whether something is more likely to be a daffodil or a flower. Anomalous
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questions invite re-interpretations. At least in a general Conversation, way, other authors Consciousness, have also and invoked Conjunctions Grice's (1975) rules of conversation in order to suggest that subjects may interpret "Linda is a bank teller" to mean "Linda is a teller and not active in the feminist movement," an entirely absolving interpretation (Macdonald, 1986; Markus & Zajonc, 1985). Indeed, there is evidence that some subjects do (Morier & Borgida, 1984; Yates & Carlson, 1986). None of these studies, however, has systematically applied and examined a Gricean analysis of conversational implicature or analyzed the several representations on which subjects may choose the conjunction and at the same time evade fallacy. The Approach We examine the degree to which subjects form and use absolving and implicating interpretations of the conjunct under the sway of Gricean conversational assumptions--interpretations at the moment of judgment that are consciously represented and subject to assessment by verbal reports and establishment by sentences read. In doing so, we are guided by three assumptions: (1) In consciousness we can represent likelihood or relative likelihoods of events, or beliefs asserting those likelihoods, and in this way they are introspectively reported in standard tests of judgment in many experiments. By the same token, it is in momentary consciousness that subjects represent interpretations on which those judgments are made, and hence they can also be assessed with verbal reports and experimentally established with verbal assertions. As always, the credibility of these indices will reflect the degree to which two kinds of considerations are met: The conscious contents are within limits of memory, linguistic expression, and disposition to report. And the obtained experimental relationships follow selectively and gracefully from hypotheses of the behavior of those contents (Dulany, 1984; Dulany, Carlson, & Dewey, 1984; Ericsson & Simon, 1984). (2) We properly call a process of judgment fallacious if it violates some normative rule of logical or mathematical inference in reaching a conclusion of the subject from premises of the subject. This is a long respected principle in the study of reasoning (Henle, 1962) that places fallacious reasoning where we think it belongs: in the reasoner's inferential operations rather than in a departure from someone else's interpretation of the conclusions or premises. The broader view, of course, is that rationality lies in normative operations of inference and decision, and irrationality in a deficiency of those deliberative operations, not in the failure of normative models to fit behavior viewed from the outside. Consider, for example, one person telling another that "Some As are Bs" and "All Bs are Cs," concluding that "As are Cs." The listener would indeed commit a fallacy by endorsing that conclusion if it were understood to say that "All As are Cs." But there is nothing fallacious or irrational in accepting that conclusion on the understanding that it means that "Some As are Cs"--regardless of how an experimenter or anyone else thinks that conclusion ought to be understood. Mathematically, there is no violation of the extension rule in saying that P(B) > P(A) except on the interpretation that B is included in the extension of A. Psychologically, by the same token, there should be no violation of the conjunction rule in saying that "teller and feminist" is more probable than "teller," except on the psychological interpretation that "teller and femi- nist" (A&B) is included in the extension of "teller," (A). Only in that case would we impeach the quality of the inferential operations. Formally, to be sure, T can be set equivalent to [(T&F) or (T¬F)]; psychologically it may or may not be. Tversky and Kahneman (1983, pp. 299, 304) evidently respect this principle, too, at least when they distinguish "fallacies and misunderstandings" and when they are at pains to argue that their subjects did not interpret "Linda is T" to mean that "Linda is T&(notF)," conceding that no conjunction fallacy would follow upon that interpretation. Therefore, only if subjects give the conjunct a particular extensional interpretation--"Linda is T" means "Linda is T&(F or notF)"--could we properly say that a
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subject's conjunction effect is a conjunction fallacy.
Conversation, Consciousness, and Conjunctions
(3) We all use representativeness in everyday judgments, and subjects are likely to do the same in this task, whether or not their conversational assumptions absolve their judgments of fallacy. Because things that are somehow alike often do behave somehow alike, we can expect subjects to know that and remember it when experimental tasks have been designed to remind them. Some who judge the conjunction more probable than the conjunct could be overwhelmed by representativeness despite according the conjunct its extensional meaning of T&(F or notF), thus committing the conjunction fallacy. Others could make the same judgment based on an equally compelling sense of representativeness while assuming that the conjunct meant that Linda is T&(notF)--or any of a number of other absolving possibilities. Our aim, therefore, is not to challenge the use of the representativeness heuristic, but to challenge common assumptions about how it works and when its consequences are fallacious and irrational. Conversational Implicature and the Conjunction Task. As a form of judgment under uncertainty, conversational inference has many of the general characteristics of inductive inference (Levinson, 1983; Sperber & Wilson, 1986). Hearers must often go beyond the information given explicitly in order to hypothesize a speaker's intended meaning. Just as theories are under-determined by data, so the number of explanatory hypotheses for an utterance is indefinitely large. It is therefore helpful for the hearer to rely on certain higher-order assumptions about the nature of conversation in the broad sense of linguistic interaction. Logicians and linguists have expended considerable effort in formulating these higher-order assumptions (for reviews, see Levinson, 1983; Sperber and Wilson, 1986). And the most influential and best known formulation, that of Grice (1975), is the one we shall employ here. Grice (1975) proposed that speakers observe a higher-order principle of cooperativeness, from which four conversational maxims follow. These are the maxims of quality, quantity, relevance, and manner (Table 1). According to these maxims, speakers will generally try to make the most informative Table 1 Grice's Co-operative Principle and Maxims of Conversation The Co-operative Principle Make your contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged. The Maxim of Quality Try to make your contribution one that you believe to be true, specifically: (1) Do not say what you believe to be false.(2) Do not say that for which you lack adequate evidence. The Maxim of Quantity (1) Make your contribution as informative as is required for the current purposes of the exchange. (2) Do not make your contribution more informative than is required. The Maxim of Relevance Make your contributions relevant. The Maxim of Manner (1) Avoid obscurity.(2) Avoid ambiguity.(3) Be brief.(4) Be orderly.
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statement (quantity) about the topic under discussion (relevance) Conversation, whileConsciousness, not saying something and Conjunctions they know to be false (quality) or unintelligible (manner). Even if scrupulous observance of these constraints should be too donnish for all discourse, they may be frequently enough honored to be built into the expectations of ordinary hearers, and it is those expectations rather than the social reality that would constrain understanding. If hearers generally feel entitled to assume that the messages they receive were constructed on these precepts, there should be interesting questions of interpretation when a speaker asserts that "Linda is bank teller." The hearer may infer that this is the most information the speaker can assert with confidence, observing the maxim of quality. But in context of an accompanying statement that "Linda is a bank teller and is active in the feminist movement," "Linda is a bank teller" is ambiguous in its implication. In particular, the statement could evoke either of two types of implicature (for full discussion, see Levinson, 1983, pp. 132-147): K-implicature: The speaker knows that the stronger assertion is not the case; for example, Linda is a bank teller and not a feminist. P-implicature: The speaker does not know whether the stronger assertion is or is not the case, and hence it is only possible; for example, Linda is a bank teller, and she may or may not be a feminist. All would now agree that the K-implicature yields an absolving interpretation: There is no fallacy in judging it more likely that Linda is than is not a feminist along with being a teller. But whether the P-implicature conveys an absolving or implicating interpretation should depend, we think, upon the sense of possibility understood by the hearer. Possibility: Epistemic, Empirical, and Logical. What comes immediately to mind are three commonsense notions of possibility widely discussed in the philosophical literature (Aune, 1967). To believe there is an empirical possibility is simply to believe that something could happen in the world we know. Empirical possibility is always constrained by evidence, and in its conscious representation by theoretical plausibility as well. As Bunge (1976) notes, we can generally assign probability values to empirical possibilities, and the English vocabulary of possibility expresses many of these distinctions (Davies, 1988). We can even think it more probable that an event occurs with one probability than with another, as when we judge it more probable that rain has probability 1 on monsoon days than probability .4. Given the context, we think, some subjects may interpret "Linda is a bank teller" as asserting that she is a teller with certainty, but that being a feminist has some probability less than one. In essence, we propose that some subjects assign probabilities reflecting their beliefs in two propositions, one asserting the certainty of Linda's being a feminist, T&(FwithP=1), and one asserting less than certainty, T&(FwithP
