Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias Toward the Ignorance Prior

Authors:
Craig R. Fox;Robert T. Clemen
Affiliations:
The Anderson School of Management and Department of Psychology, University of California at Los Angeles, Los Angeles, California 90095-1481;Fuqua School of Business, Duke University, Box 90120, Durham, North Carolina 27708-0120
Venue:
Management Science
Year:
2005

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Abstract

Decision and risk analysts have considerable discretion in designing procedures for eliciting subjective probabilities. One of the most popular approaches is to specify a particular set of exclusive and exhaustive events for which the assessor provides such judgments. We show that assessed probabilities are systematically biased toward a uniform distribution over all events into which the relevant state space happens to be partitioned, so that probabilities are "partition dependent." We surmise that a typical assessor begins with an "ignorance prior" distribution that assigns equal probabilities to all specified events, then adjusts those probabilities insufficiently to reflect his or her beliefs concerning how the likelihoods of the events differ. In five studies, we demonstrate partition dependence for both discrete events and continuous variables (Studies 1 and 2), show that the bias decreases with increased domain knowledge (Studies 3 and 4), and that top experts in decision analysis are susceptible to this bias (Study 5). We relate our work to previous research on the "pruning bias" in fault-tree assessment (e.g., Fischhoff et al. 1978) and show that previous explanations of pruning bias (enhanced availability of events that are explicitly specified, ambiguity in interpreting event categories, and demand effects) cannot fully account for partition dependence. We conclude by discussing implications for decision analysis practice.