Abstract

The present thesis consists of four chapters. The first chapter provides a summary of the three studies on strategyproof allocation rules on restricted domains.
In the second chapter, we consider the problem of allocating two public “bads” on two adjacent streets by two disjoint sets of agents with additive single dipped preferences. We show that any voting rule or social choice function (SCF) satisfying strategyproofness, streetwise Pareto optimality, and independence of irrelevant alternatives assigns extreme points to each profile. Moreover, such SCF or voting rule is decomposable- location of a street is determined solely by the residents of that street.
In the third chapter, I consider the problem of allocating two public “bads’’ on two adjacent streets with multi-dimensional single-dipped preferences. Each agent has a worst location on both streets. We show that any strategyproof social choice function (SCF) or voting rule satisfying Pareto optimality and independence of irrelevant alternatives selects only the extreme points of the streets as the locations of the public facilities.
In the fourth chapter, I consider the problem of allocating a perfectly divisible commodity among a group of agents with single dipped preferences. I study a subdomain of single dipped preferences and identify a sub-domain that I call the (h*, k*)-dip restricted domain. On that domain, I found that Pareto optimality and equal treatment of equals are compatible. I show that on this restricted domain, the equal sharing rule is the only rule satisfying strategyproofness, Pareto optimality and equal treatment of equals.