From overconfidence to pragmatic implicatures: How people describe uncertain quantities
When people are asked to describe uncertain quantities (the price for a flight to Glasgow, the time it will take to get an editorial response), they can answer by offering a range (£150-250, 3-5 months). Such intervals are often too tight. 90% confidence intervals typically lead to hit rates of only 50-60%. Most debiasing attempts have not been very successful. We found, however, that people demonstrate confidence neglect, producing the same interval regardless of the assigned level of confidence. It appears, moreover, that they are not very confident in their own confidence intervals. In daily life uncertainty is often expressed not as complete ranges, but as single lower limit or single upper limit estimates: “The ticket will cost at least £150”. Such “one-sided intervals” have not been systematically explored. We have studied two aspects of the psychology of one-sided intervals: (a) How interval width is influenced by inclusive versus exclusive terms, and (b) Which pragmatic inferences are drawn from lower versus upper limit estimates. (a) Interval bounds appear to be of two kinds: Inclusive, where the upper or lower limits are included in the interval (e.g., minimum and maximum values); or exclusive, where they are outside the interval (more than X, less than Y). These phrases give rise to different intervals. It turns out that exclusive intervals are much wider than inclusive intervals for estimates of single target values (e.g. prices of specific items). For distributions (variable values) we discovered the opposite effect. (b) Lower and upper interval estimates give rise to pragmatic inferences. A person who estimates that a pair of shoes will cost “over £40” (or “minimum 40”), provides the listener with a provisional reference point, and asserts that the target value is above this point, implying that the shoes are expensive. An upper limit estimate (“under £80”) implies, by the same token, that the shoes are cheap. In contrast, the most likely value (“about £60”) may be numerically more informative, but is less informative from an evaluative point of view. Several studies show that people draw pragmatic inferences from upper and lower limit statements about the speaker’s attitudes, degree of optimism, and the kind of advice implied by choice of limit. They generally assume that lower limit estimates suggest that we are talking about relatively large amounts, or a growing trend, whereas upper limit estimates indicate small amounts and decreasing trends.