Strategyproof social choice for restricted domains

This thesis examines strategic manipulation in three areas of social choice theory---single-winner voting, multiwinner voting, and judgment aggregation. While we would like our aggregation methods to be strategyproof---meaning no agent has an incentive to misreport her preferences or opinions---strategic manipulation is difficult to avoid, no matter what specific framework we consider.
A well-known and often used approach is to consider only specific types of input to the aggregation method---so-called restricted domains. Our approach here is to consider manipulation on profiles that fall within certain restricted domains where existing results tell us manipulation within the domain is not possible. In general we ask whether agents can manipulate from a profile in a "well-behaved" domain to one outside the domain in question.
By showing that an aggregation method is strategyproof in this sense, we show that allowing all inputs will not create unnecessary possibilities for manipulation. Thus, our work is an argument against restricting the domain of the aggregation method. We also aim to understand how strategyproofness on these domains can interact with the axiomatic properties of our aggregation methods.
Chapters 3, 4, and 5 each focus on this larger question in a different framework within the area of social choice. Chapter 3 looks at (single-winner) voting, focusing on the domain of profiles with a Condorcet winner. Chapter 4 considers approval-based multiwinner voting, where we study strategyproofness on party-list profiles. Chapter 5 discusses strategyproofness of majoritarian judgment aggregation rules on profiles with a consistent majority.