Thesis advisor: Uzi Segal / This dissertation consists of three chapters analyzing preferences for randomization in social choice problems. The first two chapters are related and in the fields of distributive justice and social choice. They concern allocation of an indivisible good in social choice problems where efficiency is at odds with equality. The last chapter addresses a social choice problem from an individual's perspective using decision theoretical analysis. In this dissertation I demonstrate why randomization may be an attractive policy in social choice problems and demonstrate how individuals may have preferences over the precise method of randomization. The first chapter is titled "Live and Let Die." This paper discusses how to allocate an indivisible good by social lottery when agents have asymmetric claims. Intuition suggests that there may exist agents who should receive zero probability in the optimal social lottery. In such a case, I say that these agents have weak claims to the good. This paper uses a running example of allocating an indivisible medical treatment to individuals with different survival rates and reactions to the treatment in order to provide conditions for consistency of weak claims. As such, I develop two related assumptions on a social planner's preferences over lotteries. The first -- survival rate scaling -- states that if an individual has a weak claim, then his claim is also weak when survival rates increase proportionally. The second -- independence of weak claims -- states that if an individual has a weak claim, then his removal does not affect others' probabilities of receiving the treatment. These assumptions imply that a compatible social welfare function must exhibit constant elasticity of substitution, which results in potentially-degenerate weighted lotteries. The second chapter is titled "Why is Six Afraid of Seven? Bringing the "Numbers" to Economics." This chapter discusses the numbers problem: the question of if the numbers of people involved should be used to determine whether to help certain people or to help certain other people. I discuss the main solutions that have been proposed: flipping a coin, saving the greater number, and proportionally weighted lotteries. Using the economic tools of social choice, I then show how the model of the previous chapter, "Live and Let Die," can be extended to address numbers problems and compare the implications of prominent social welfare functions for numbers problems. I argue that potentially-degenerate weighted lotteries can assuage the main concerns discussed in the literature and I show that both the Nash product social welfare function as well as constant elasticity of substitution (CES) social welfare functions are compatible with this solution. Finally, I discuss a related problem known as "probability cases," in which individuals differ in survival chances rather than numbers of individuals at risk. When the model is extended to allow for both asymmetries in survival chances and numbers of individuals in groups, CES results in potentially-degenerate weighted lotteries whereas Nash product does not. The third chapter is titled "All Probabilities are Equal, but Some Probabilities are More Equal than Others," which is joint work with Professor Uzi Segal of the Economics Department at Boston College and Professor Shlomo Naeh of the Departments of Talmud and Jewish Thought at The Hebrew University of Jerusalem. In this chapter we compare preferences for different procedures of selecting people randomly. A common procedure for selecting people is to have them draw balls from an urn in turn. Modern and ancient stories (for example, by Graham Greene and the Talmud) suggest that such a lottery may not be viewed by the individuals as "fair.'' In this paper, we compare this procedure with several alternatives. These procedures give all individuals equal chance of being selected, but have different structures. We analyze these procedures as multi-stage lotteries. In line with previous literature, our analysis is based on the observation that multi-stage lotteries are not considered indifferent to their probabilistic one-stage representations. As such, we use a non-expected utility model to understand the preferences of risk-averse individuals over these procedures and show that they may be not indifferent between them. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.