Essays on social choice and object allocation

This collection of essays studies the properties of collective decision procedures when monetary compensation is unavailable. The first three chapters consider abstract social choice settings, emphasizing solidary and strategic properties of rules. The final chapter narrows the focus to object allocation and investigates efficiency and strategic properties.;Broadly, solidarity requires that, when some aspect of the environment changes, all individuals are affected similarly, either sharing the benefits or losses. Recognising other individuals as a relevant component of one's environment, we apply this principle to changes in the population or preferences of other individuals. Narrowing our solidarity requirement, our properties ask that individuals be affected in the same direction, avoiding only those cases in which some gain while others lose.;Chapter 1 begins our study of social choice. When choosing between two alternatives, we find that only rules satisfying our solidarity requirements and efficiency require consensus: Each rule selects pre-determined alternative unless all individuals prefer the other. We further derive logical relationships among solidarity and strategic properties extend the model to accommodate individuals who are indifferent between the alternatives. Moving beyond the binary setting, we quickly reach an impossibility: No efficient rules satisfy our solidarity property.;Chapter 2 moves to preference aggregation. Supposing that individuals report rankings over alternatives, we adopt a conservative approach to infer limited preferences over orders. Adapting the solidarity principle to the resulting incomplete preferences, we formulate new axioms requiring solidarity when the preferences of some agents chance. Although the most general requirement proves incompatible with efficiency, restriction to the smallest change in preferences, transposition of a single pair of alternatives, leads to a characterization of the ``status quo'' rules. We further extend these rules to allow indifferences in the status quo order and offer a simple algorithm to apply these rules.;Chapter 3 considers another specialized model of social choice, the problem of choosing the level of a public good when individuals have single-peaked preferences over the feasible levels. Imposing a measure on the space of preferences, we introduce a parameterized family of solidarity axioms which restrict the conclusion to preference changes below a threshold size. With these axioms, we test the robustness of previous results characterizing the ``target'' rules by efficiency and unrestricted solidarity axioms. In fact, together with efficiency, each restricted axiom also characterizes the target rules.;Moving away from social choice, Chapter 4 studies to object allocation. In this setting, we propose to evaluate rules by their performance ex-ante, before individuals learn their own preferences. To do so, we introduce an appropriate strengthening of efficiency which applies at the ex-ante stage and identify rules satisfying this property. When combined with standard incentive properties, our efficiency notion characterizes the family of priority rules. However, the negative implications of this narrow are tempered in symmetric environments where we find that other incentive-compatible rules achieve the same utilitarian welfare as the priority rules and lead to more equitable distributions of expected utility.