A paradox for tiny probabilities and enormous values

Abstract

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. Reckless theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; timid theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; non-transitive theories deny the principle that, if (Formula presented.) is better than (Formula presented.) and (Formula presented.) is better than (Formula presented.), then (Formula presented.) must be better than (Formula presented.). 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.