| In the first two chapters, we introduce a model of a mixed-good economy where agents have single-peaked preferences. Decomposing the mixed good into two components, a private good and a public good, we restrict the domain to separably single-peaked and lexicographic preferences, where the private good is the primary concern of any agent. An allocation is both a public good level—which is also the total amount available for the private good—and a distribution of this public good among the agents. In the first chapter, we describe the set of efficient allocations and add the no-envy requirement, proving that a uniform distribution must be used at any peak-only selection from that set. We then obtain characterizations of two efficient and envy-free rules that use a uniform distribution: one that satisfies resource-monotonicity and selects the associated minimum efficient public good level, and another that satisfies consistency and peak-only and that, whenever feasible, gives every agent his private peak.; In the second chapter, we focus on single-valued rules and conduct an analysis of the implications of strategy-proofness and efficiency. Adding the requirements of continuity and symmetry, we prove that any rule satisfying this set of properties must use a uniform distribution. We then extract the additional implications of this set of properties and conclude that they are less demanding with respect to the choice of the public good level, allowing for but not requiring the use of the uniform generalized median-voter rule. Both strategic and normative concerns lead us however to a clear recommendation: the use of a uniform distribution, regardless of the associated choice for the public good level.; In the last chapter, we analyze single binary-choice voting rules and identify the presence of the No-Show paradox in this simple setting, as a consequence of specific turnout conditions included in actual rules that are meant to ensure a representative outcome. We formalize this concern and conclude that no voting rule can ensure representation if non-voting is possible, unless restrictive assumptions are made on the preference domain of non-voters. We recommend that a conscious choice be made on how non-voting is to be interpreted and that this choice be used to derive the corresponding referendum rule. |
