A paradox for tiny probabilities and enormous values

We begin by showing that every theory of the value uncertain prospects must have one three unpalatable properties. Reckless theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance enormous gain; timid permit passing large potential gain to prevent increase in risk; non-transitive deny principle that, if A is better than B and C, then be C. Having set this trilemma, we study its horns. Non-transitivity has been much discussed; focus on drawing out costs benefits recklessness timidity when it comes axiology, decision theory, normative uncertainty.