Petra Kosonen

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion on Independence generalizes to other views that also violate Independence.

According to Longtermism, our acts’ expected influence on the expected value of the world is mainly determined by their effects in the far future. There is, given total utilitarianism, a straightforward argument for Longtermism due to the enormous number of people that might exist in the future, but this argument does not work on person-affecting views. In this paper, we will argue that these views might also lead to Longtermism if Prudential Longtermism is true. Prudential Longtermism holds for a person if and only if our acts’ overall influence on that person’s expected well-being is mainly determined by the acts’ effects in the far future. We argue that (due to a small chance of anti-ageing and uploading) there could be an enormous amount of prudential value for some contemporary person in the far future and that value may be so large that it dominates their overall expectation of lifetime well-being.

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero probability. Chapters 3–6 discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future.

Derek Parfit argues that fission is prudentially better for you than ordinary death. But is having more fission products with good lives prudentially better for you than having just one? In this paper, we argue that it is. We argue that, if your brain is split and the halves are transplanted into two recipients, then it is prudentially better for you if both transplants succeed than if only one of them does. This upshot rules out, among other things, that the prudential value of standing in the relation that matters in survival to multiple people is equal to their average well-being.

Nebel argues for the Repugnant Conclusion via the “Intrapersonal Repugnant Conclusion,” on which certainty of a mediocre life is better for individuals than a sufficiently small chance of an excellent life. In this article, I deny that acceptance of the Intrapersonal Repugnant Conclusion leads us to the Repugnant Conclusion. I point out that on many views which avoid the Repugnant Conclusion we should discount very small probabilities down to zero. If we do, then Nebel’s crucial premise of Ex Ante Pareto fails, because discounting at the individual level can fail to match up with discounting at the population level.