Postdoctoral Fellow at the Population Wellbeing Initiative,
University of Texas at Austin
Tiny Probabilities of Vast Value
Thesis, University of Oxford, 2022 Link to Oxford University Research Archive
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.
Discounting Small Probabilities Solves the Intrapersonal Addition Paradox
Ethics 132(1), pp. 204–217 (2021) Link to journal website
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.
Do Lefty and Righty Matter More than Lefty Alone?
Erkenntnis (2022), with Johan E. Gustafsson. Link to journal website
Do Lefty and Righty Matter More Than Lefty Alone?
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 (who both have good lives), then it is prudentially better for you if both transplants succeed than if only one of them does (other things being equal). 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.
Bounded Utilities and Ex Ante Pareto
This paper shows that decision theories on which utilities are bounded, such as standard axiomatizations of Expected Utility Theory, violate Ex Ante Pareto if combined with an additive axiology, such as Total Utilitarianism. A series of impossibility theorems point toward Total Utilitarianism as the right account of axiology, while money-pump arguments put Expected Utility Theory in a favorable light. However, it is not clear how these two views can be reconciled. This question is particularly puzzling if utilities are bounded (as standard axiomatizations of Expected Utility Theory imply) because the total quantity of well-being might be infinite or arbitrarily large. Thus, there must be a non-linear transformation from the total quantity of well-being into utilities used in decision-making. However, such a transformation leads to violations of Ex Ante Pareto. So, the reconciliation of Expected Utility Theory and Total Utilitarianism prescribes prospects that are better for none and worse for some.
Probability Discounting and Money Pumps
In response to cases that involve very small probabilities of huge payoffs, some argue that we ought to discount very 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. However, this paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities.
OVERVIEW of probability fanaticism (Introduction to my thesis)
This paper explores different approaches to cases that involve tiny probabilities of huge payoffs. The main approaches discussed are Probability Fanaticism, Boundedness and Probability Discounting. First, the paper discusses two arguments for maximizing expected utility: the long-run argument and representation theorems. Next, it investigates Probability Fanaticism, on which tiny probabilities of huge positive or negative payoffs can have enormous positive or negative expected utility (respectively). Various arguments for and against Probability Fanaticism are discussed. Then, the paper considers Boundedness, namely, the idea that utilities are bounded. Finally, the paper discusses Probability Discounting, on which tiny probabilities should be ignored in practical decision-making. Some other approaches are also discussed briefly. The paper concludes that the paradoxes involving tiny probabilities of vast value show that some intuitively compelling principles of rationality must be given up.
Prudential Longtermism (with Johan E. Gustafsson)
According to Longtermism, our acts’ expected influence on the value of the world is mainly determined by their effects in the far future. Given additive axiologies, such as total utilitarianism, there is a straightforward argument for Longtermism due to the enormous number of people that may exist in the future. This argument, however, does not work on person-affecting views. In this paper, we will argue that these views may, in fact, also lead to Longtermism. The reason they may do so is that Prudential Longtermism may be true. Prudential Longtermism holds for you if and only if our acts’ overall influence on your expected well-being is mainly determined by their effects in the far future. We argue that (due to a combination of anti-ageing, cryonics, uploading, and biological uploading) there could be an enormous amount of prudential value for you in the far future. This potential value may be so large that it dominates your overall expectation of lifetime well-being.
How to discount small probabilities
Maximizing expected value leads to counterintuitive choices in cases that involve tiny probabilities of huge payoffs. In response to such cases, some have argued that we ought to discount very small probabilities down to zero. In this paper, I discuss how exactly this view can be formulated. I begin by showing that less plausible versions of discounting small probabilities violate dominance. Then, I show that more plausible formulations of this view avoid these dominance violations, but instead, they violate the axiom of Independence. As a result of this violation, those who discount small probabilities can be exploited by a money pump. I conclude that discounting small probabilities faces significant problems that undermine its plausibility as a theory of instrumental rationality.
Tiny Probabilities and the Value of the Far Future
Morally speaking, what matters the most is the far future—at least according to Longtermism. The reason why the far future is of utmost importance is that our acts’ expected influence on the value of the world is mainly determined by their consequences in the far future. The case for Longtermism is straightforward: Given the enormous number of people who might exist in the far future, even a tiny probability of affecting how the far future goes outweighs the importance of our acts’ consequences in the near term. However, it seems that there is something wrong with a theory that lets very small probabilities of huge payoffs dictate one’s course of action. If instead, we discount very small probabilities down to zero, we may have a response to Longtermism provided that its truth depends on tiny probabilities of vast value. Contrary to this, I will argue that discounting small probabilities does not undermine Longtermism.
Expected Utility Theory and Possible States of Zero Probability
At least at first glance, Expected Utility Theory tells us to be indifferent between two prospects when they are otherwise the same, except that one gives a better outcome than the other in a possible state of zero probability. But as some have suggested, Expected Utility Theory might be supplemented with dominance to get the verdict that the dominating prospect is better than the dominated one. However, I will show that if Expected Utility Theory is supplemented with dominance in this way, it will violate the Continuity axiom of Expected Utility Theory.
Ignore Outlandish Possibilities (with Tomi Francis)
Expected Utility Theory appears to face two problems. The first one is the Problem of Outlandishness: Our decisions could depend almost entirely on what happens if very outlandish things are true. The second problem is that once we consider gambles with infinitely many possible outcomes, Expected Utility Theory either needs to be bounded, or it will be inconsistent with an infinitary generalisation of the Sure Thing Principle leaving it vulnerable to money pumps. But, Bounded Expected Utility Theory is very difficult to believe in the moral case: It is hard to believe that
there could ever be a case where it would be better to save some number of lives for sure than it would be to save any number of lives with probability almost one. In order to solve these two problems, we propose that we should conditionalise on the falsity of outlandish propositions before applying Expected Utility Theory. We suggest two accounts of outlandishness, however, both versions suffer from serious objections. The most significant of these is that both seem to leave an agent vulnerable to money pumps.
A dialogue based on Pascal’s Mugging.
For all of the following courses, I chose the topics covered in tutorials, assigned the readings for them and decided the weekly essay questions. I was also responsible for giving the final grade to some of the students.
St. Catherine’s College, University of Oxford, 2021
I taught one-on-three tutorials on ethics.
St. Catherine’s College, University of Oxford, 2021
I taught tutorials on practical ethics for one student.
Theory of Politics
University College, University of Oxford, 2021
I taught one-on-one and one-on-two tutorials on political philosophy for three students.