Conversing under Uncertainty

Conversing under Uncertainty

The representativeness heuristic generally favors outcomes that make good stories or good hypotheses. The conjunction feminist bank teller is a better hypothesis about Linda than bank teller, and the scenario of a Russian invasion of Poland followed by a diplomatic crisis makes a better story than simply diplomatic crisis. The notion of a good story can be illuminated by extending the Gricean concept of cooperativeness (Grice, 1975) to conversations under uncertainty. The standard analysis of conversation rules assumes that the speaker knows the truth. The maxim of quality enjoins him or her to say only the truth. The maxim of quantity enjoins the speaker to say all of it, subject to the maxim of relevance, which restricts the message to what the listener needs to know. What rules of cooperativeness apply to an uncertain speaker – that is, one who is uncertain of the truth? Such a speaker can guarantee absolute quality only for tautological statements (e.g., “Inflation will continue so long as prices rise”), which are unlikely to earn high marks as contributions to the conversation. A useful contribution must convey the speaker’s relevant beliefs even if they are not certain. The rules of cooperativeness for an uncertain speaker must therefore allow for a trade-off of quality and quantity in the evaluation of messages. The expected value of a message can be defined by its information value if it is true, weighted by the probability that it is true. An uncertain speaker may wish to follow the maxim of value: Select the message that has the highest expected value.

The expected value of a message can sometimes be improved by increasing its content, although its probability is thereby reduced. The statement, “Inflation will be in the range of 6% to 9% by the end of the year” may be a more valuable forecast than, “Inflation will be in the range of 3% to 12%,” although the latter is more likely to be confirmed. A good forecast is a compromise between a point estimate, which is sure to be wrong, and a 99.9% credible interval, which is often too broad. The selection of hypotheses in science is subject to the same trade-off. A hypothesis must risk refutation to be valuable, but its value declines if refutation is nearly certain. Good hypotheses balance informativeness against probable truth (Good, 1971). A similar compromise obtains in the structure of natural categories. The basic level category dog is much more informative than the more inclusive category animal and only slightly less informative than the narrower category beagle. Basic-level categories have a privileged position in language and thought, presumably because they offer an optimal combination of scope and content (Rosch, 1978). Categorization under uncertainty is a case in point. A moving object dimly seen in the dark may be appropriately labeled dog whereas the subordinate beagle would be rash and the superordinate animal far too conservative.

Consider the task of ranking possible answers to the question, “What do you think Linda is up to these days?” The maxim of value could justify a preference for T&F over T in this task, because the added attribute feminist considerably enriches the description of Linda’s current activities at an acceptable cost in probable truth. Thus, the analysis of conversation under uncertainty identifies a pertinent question that is legitimately answered by ranking the conjunction above its constituent. We do not believe, however, that the maxim of value provides a fully satisfactory account of the conjunction fallacy. First, it is unlikely that our respondents interpret the request to rank statements by their probability as a request to rank them by their expected (informational) value. Second, conjunction fallacies have been observed in numeric estimates and in choices of bets, to which the conversational analysis simply does not apply. Nevertheless, the preference for statements of high expected (informational) value could hinder the appreciation of the extension rule. As we suggested in the discussion of the interaction of picture size and real size, the answer to a question can be biased by the availability of an answer to a cognate question – even when the respondent is well aware of the distinction between them.

The same analysis applies to other conceptual neighbors of probability. The concept of surprise is a case in point. Although surprise is closely tied to expectations, it does not follow the laws of probability (Kahneman & Tversky, 1982b). For example, the message that a tennis champion lost the first set of a match is more surprising than the message that she lost the first set but won the match, and a sequence of four consecutive heads in a coin toss is more surprising than four heads followed by two tails. It would be patently absurd, however, to bet on the less-surprising event in each of these pairs. Our discussions with subjects provided no indication that they interpreted the instruction to judge probability as an instruction to evaluate surprise. Furthermore, the surprise interpretation does not apply to the conjunction fallacy observed in judgment of frequency. We conclude that surprise and informational value do not properly explain the conjunction fallacy, although they may well contribute to the ease with which it is induced and to the difficulty of eliminating it.