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'Totalism' in population axiology is the view that one population is better than another if and only if it contains greater total wellbeing. This thesis defends Totalism. I begin, in Chapter 1, by arguing for the principle of Anonymity, according to which any two populations with the same anonymous distribution of wellbeing are equally good. Chapter 2 argues against Prioritarian population axiologies on the basis that they imply the 'desirability of welfare diffusion': the implausible claim that it can be better for there to be less total wellbeing spread thinly between a larger total number of people. Chapter 3 argues against the popular intuition that adding good lives within a certain range cannot result in a better population. Chapters 4 and 5 provide new evidence for the unavoidability of the Repugnant Conclusion, the controversial implication of Totalism which holds that a smaller population of excellent lives can be worse than a much larger population of mediocre lives (and which is traditionally considered to be a damning objection to Totalism). Chapter 6 argues for a version of Totalism applicable to prudence in fission cases: cases where an individual "splits" into two or more successors, while retaining what matters in survival. Finally, Chapter 7 ties things together and summarises several direct arguments for Totalism. With the exception of Chapter 7, which makes extensive use of results and notation from earlier parts of the thesis, each chapter is entirely self-standing and can be read independently of the others.

This thesis examines three philosophical topics relevant to the project of identifying and acting on the most effective ways of doing good: anthropic reasoning, simulation arguments, and infinite ethics. These topics are unified in their potential to disrupt the empirical and normative assumptions underlying the most straightforward case for "strong longtermism" (that is, the view that positively influencing the long-term future is the key moral priority of our time). The first chapter examines the debate between the Self-Indication Assumption ("SIA") and the Self-Sampling Assumption ("SSA") in the context of anthropic reasoning - a debate with important implications for the size of humanity's future (and, plausibly, of the universe itself). I argue that SIA is the superior view, and that the most prominent objection to SIA - the so-called "Presumptuous Philosopher" - is a bullet that we should consider biting. The second chapter formulates what I see as the strongest version of a "simulation argument" - that is, an argument that we should be highly confident that at least one of the following is true: either the ratio of simulated beings ("sims") to non-simulated beings ("non-sims") of certain types is not high, or we are sims. I distinguish between ways of making this argument that rely on empirical assumptions (for example, about the computational power available to advanced civilizations) and those that do not; I suggest that the latter are superior and independently forceful; and I explore some of the complications and uncertainties that the latter lead to. The third chapter surveys a variety of problems that infinities create for ethics, and it reflects on the implications of those problems. In particular, I argue that these problems puncture the dream of a simple, bullet- biting utilitarianism, and that they put pressure on some of the broader intuitions underlying common arguments for strong longtermism as well.