Estimating the probability of negative events Adam J.L. Harris * , Adam Corner, Ulrike Hahn Department of Psychology, Cardiff University, Tower Building, Park Place, Cardiff CF10 3AT, United Kingdom article info Article history: Received 17 January 2007 Revised 7 October 2008 Accepted 10 October 2008 Available online xxxx Keywords: Probability Utility Severity Asymmetric loss functions Control abstract How well we are attuned to the statistics of our environment is a fundamental question in understanding human behaviour. It seems particularly important to be able to provide accurate assessments of the probability with which negative events occur so as to guide rational choice of preventative actions. One question that arises here is whether or not our probability estimates for negative events are systematically biased by their severity. In a minimal experimental context involving an unambiguous, objective representation of probability, we found that participants judged a controllable event as more likely to occur when its utility was extremely negative than when it was more neutral. A deci- sion-theoretic explanation based on loss function asymmetries is advanced which supports the claim that probability estimates are not intrinsically biased by utilities. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Decision theory (Pratt, Raiffa, & Schlaifer, 1995) posits that when selecting between alternative courses of action, individuals should select the alternative with the greatest expected benefit – that is, individuals should seek to max- imise the subjective expected utility of their choice. The normative principles of decision theory dictate that the assessment of an outcome’s expected utility should be based on how probable that outcome is perceived to be (the expectancy component), and the subjective value attached to that outcome (the utility component). Our decision about whether or not to carry an umbrella, for example, should be based on how likely we think it is that it will rain and how bad it would be if we were to get wet, compared to the irritation of carrying an umbrella with us unnecessarily if, in fact, it did not rain. Within this frame- work, probabilities and utilities are assumed to be inde- pendent constructs. Intuitively, one might not expect an individual’s estimate of the chance of rain to be based on their judgment of how bad it would be if they got caught without an umbrella. However, there is a long history of re- search querying whether probabilities and utilities are in fact assessed independently. 1.1. Estimating probabilities Early research on decision-making (Crandall, Solomon, & Kellaway, 1955; Edwards, 1953, 1962; Irwin, 1953; Marks, 1951; Morlock & Hertz, 1964) gave some grounds for believing that people’s estimates of an event’s probability are influenced, to some extent, by the event’s utility. How- ever, these initial studies typically used choice paradigms, and thus assessed probability judgments only indirectly. Given that choice is governed by both probability and util- ity, and that both of these factors can simultaneously and subjectively vary, it is very hard to isolate either factor using such an approach. Hence, the results from studies uti- lising decision-making paradigms can generally be ex- plained in terms of non-linear utility functions (e.g., Kahneman & Tversky, 1979). No interdependence between probability and utility is therefore necessary to account for these findings (see also Edwards, 1962; Slovic, 1966). Some support for the idea that utilities influence prob- ability estimates emerges from research into the subjective interpretation of probability words (e.g., Weber & Hilton, 1990). The concept of probability is inherently numerical, yet we often communicate probabilities through verbal 0010-0277/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cognition.2008.10.006 * Corresponding author. Tel.: +44 2920874007. E-mail address: harrisaj@cardiff.ac.uk (A.J.L. Harris). Cognition xxx (2008) xxx–xxx Contents lists available at ScienceDirect Cognition journal homepage: www.elsevier.com/locate/COGNIT ARTICLE IN PRESS Please cite this article in press as: Harris, A. J. L., et al. Estimating the probability of negative events. Cognition (2008), doi:10.1016/j.cognition.2008.10.006