Catastrophe, Compounding & Consistency in Choice

Conditional value-at-risk (CVaR) precisely characterizes the influence that rare, catastrophic events can exert over decisions. Such characterizations are important for both normal decision-making and for psychiatric conditions such as anxiety disorders - especially for sequences of decisions that might ultimately lead to disaster. CVaR, like other well-founded risk measures, compounds in complex ways over such sequences - and we recently formalized three structurally different forms in which risk either averages out or multiplies. Unfortunately, existing cognitive tasks fail to discriminate these approaches well; here, we provide examples that highlight their unique characteristics, and make formal links to temporal discounting for the two of the approaches that are time consistent. These examples can ground future experiments with the broader aim of characterizing risk attitudes, especially for longer horizon problems and in psychopathological populations. Introduction Given the many uncertainties in the present and future, we had to evolve sophisticated ways of handling risk. Individual appetites or aversion for risk differ substantially, with various forms of psychopathology arising at the extremes of these preferences. Psychology and neuroscience have focused on single risky decisions (typically just one spin of the wheel of outrageous fortune). Historically, heuristics dominated [1]; however, recently, axiomatically justifiable forms of risk sensitivity from the finance industry are starting to permeate.