This dissertation studies the efficient and fair allocation of indivisible goods without monetary transfer. It is a collection of three papers and uses school-choice programs as a motivating example. I provide theoretical results that can guide the design of new allocation systems as well as tools that can be used to enhance existing systems.

In Chapter 1, I analyze how information disclosure affects social welfare using a stylized model. In my model, the utility of agents consists of a vertical "quality" component and a horizontal "idiosyncratic taste" component. The exact qualities of the objects are unknown to the agents, and the social planner seeks an information-disclosure policy that will maximize the total utility. The results show that (1) the optimal disclosure policy hides small differences in quality and reveals large differences in quality, (2) more information is disclosed when the valuations of the quality are heterogeneous, and (3) the Immediate Acceptance mechanism is more conducive for information disclosure than the Deferred Acceptance mechanism.

In Chapter 2, I study the collocation of groups of students in school-choice programs. In particular, I examine when and how stochastic assignment matrices can be decomposed into lotteries over deterministic assignments subject to collocation constraints. I first show that---regardless of the number of pairs of twins in the student body---twin collocation can be maintained in a decomposition if one extra seat can be added to each school. I then propose a decomposition algorithm based on Column Generation that can incorporate a wide variety of constraints including collocation constraints.

In Chapter 3, I propose a new notion of fairness that combines the concept of rank values and the maximin principle. An assignment is rank-egalitarian undominated (REU) if there is no other assignment that is equally or more egalitarian for any set of rank values. I show that each REU assignment can be generated as a solution to a linear programming problem that maximizes the weighted sum of expected rank values of the worst-off agents. I also provide an algorithm that generates special subsets of REU assignments that are practically important.