A paradox for tiny probabilities and enormous values

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 𝐴 is better than 𝐵 and 𝐵 is better than 𝐶 , then 𝐴 must be better than 𝐶 . 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 reckless-ness and timidity when it comes to axiology, decision theory, and normative uncertainty.