Compensation Schemes in Collective Decision Making

Abstract

This memory consists of four independent essays on Social Choice Theory and Mechanism Design. The first two chapters are particularly related since they share the common aim of relaxing an idea of solidarity called replacement monotonicity or welfare-domination under preference-replacement proposed in the literature by Moulin (1987) and Thomson (1993, 1995a, 1 995b). Chapters 2 and 3 share the same basic model of public good provision in which no monetary compensations are allowed. Agents are assumed to have single-peaked preferences defined on a single uni-dimensional good and we try to investigate and overcome the limited number of Social Choice procedures that are replacement monotonic within this setup.<br/><br/>Chapter 2 introduces a new property of solidarity in terms of reciprocity for these environments. This property allows for a richer class of social choice procedures than Thomson's solidarity concept of welfare-domination under preference-replacement. Our proposal reflects somehow an introspective concept of solidarity. It requires that when somebody changes his preferences and the social decision is altered, all the remaining agents can be sure that the same agent who has actually changed would have been affected in a reciprocal way if they had changed likewise. Characterizations of the rules satisfying reciprocity in both a strong and a weak version are therefore provided.<br/><br/>Chapter 3 relaxes replacement monotonicity in a more direct way, understanding solidarity in the sense of the proportion of society gaining or losing together when somebody changes his preferences. It is demonstrated that solidarity is in direct conflict with other fairness criteria. Actually, achieving centrist or equitable outcomes leads to the smallest possible solidarity degree. Applying Campbell and Kelly's (1993) Trade-offTheory, we propose reasonable mesures of both solidarity and rigidity of social choice procedures and a menu of voting procedures is found to embody different degrees of both desirable properties.<br/><br/>Chapters 4 and 5 deal with the problem of finding strong incentive compatible mechanisms in two different production contexts when compensations to induce truthful behavior are allowed.<br/><br/>In Chapter 4 we deal with an implementation problem where the compensation sheme is not part of the feasible alternatives, but discretional to the planner. Within this framework, we assume that the planner or principal have the ability to partially design the functional form of the division s final payoffs to incentive their truthful behavior in the contract offered to the divisions.<br/><br/>In Chapter 5 we deal with the same problem of designing a contract between the members of a complex productive organization -say divisions within a firm- to give incentives for truthful behavior in the presence of private information about parts of the technologies. In particular, we propose a simple task allocation model known in the network programming literature as the Critical Path Method, CPM or PERT. Divisions have to undertake time-consuming tasks that have to be allocated in a network. We prove the existence in this environment of anonymous and strategy-proof mechanisms that are efficient in the sense of minimising the total amount of time employed in finalising the project and can also be balanced, so full efficiency is achieved.

Date of Award	30 Mar 2001
Original language	English
Supervisor	Salvador Barberà (Director)