Envisioning the Improbable: Judgment and Strategy in Heavy-Tailed Contexts

Abstract

Heavy-tailed probability distributions characterize many contexts of great importance to managers and entrepreneurs (e.g., sales of branded products, asset prices, and environmental phenomena). In heavy-tailed contexts, due to dependent social/networked mechanisms (e.g. preferential attachment), low-probability/high–consequence events occur relatively frequently. If these contexts are mistakenly classified as thin-tailed or approximately normally distributed (i.e., rare outcomes are exceedingly unlikely), managers may undervalue or dismiss investment opportunities, sell assets too cheaply, or fail to insure against catastrophic loss. I demonstrate, through simulation, that heavy–tailed phenomena often exhibit samples that appear thin- tailed, even for large samples or long periods. Accordingly this paper examines the judgments of individuals regarding possible extreme (low–probability/high-consequence) events in heavy–tailed contexts in the absence of representative experience. The first study demonstrates that individuals overwhelmingly fail to distinguish between heavy- and thin–tailed contexts in the absence of experience biasing their judgments towards thin-tailed distributional assumptions, thereby underweighting unusual events in heavy-tailed contexts. The second study confirms, using text analysis of individual reasoning statements, that contextual knowledge, the ability to classify heavy- tailed sample data as possibly misleading or unsuitable for inference based on context, leads to more accurate estimates of the magnitude and frequency of errors in expectations and moderates the biased judgments found in Study 1. The third study tests and validates a new method of eliciting confidence appropriate for heavy-tailed contexts ― the willingness to pay to avoid, or profit from, tail uncertainty. In the final study intermediate statistical knowledge does not appear to moderate the biased judgments found in study 1. Since accurate valuation of strategies depends on correct distributional classification (thin- or heavy-tailed) of opportunities and threats, this work has broad implications for entrepreneurs, managers, and policy-makers. The paper concludes with a brief comparison of proposed strategies appropriate for thin- vs. heavy-tailed contexts in a number of fields, along with proposals for improved performance measures, and some notes on nuanced incentive structures that may encourage the underweighting of tail events in heavy-tailed contexts and promote unethical or rogue behavior. This is the first empirical work to develop tests of individual ability to distinguish between heavy-and thin-tailed contexts and to introduce and test a method of elicitation of confidence that measures individual perceptions of the magnitude and likelihood of possible errors surrounding their expectations (i.e., tail uncertainty).