A paradox for tiny probabilities and enormous values

Abstract

AbstractWe begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties.Recklesstheories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain;timidtheories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk;non‐transitivetheories deny the principle that, ifAis better thanBandBis better thanC, thenAmust be better thanC. Having set up this trilemma, we study its horns. Non‐transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty.