Essays in Strategy-proof Social Choice Theory
This thesis consists of two separate papers in strategy-proof social choice theory. The first paper, “Generalizing the Gibbard-Satterthwaite theorem: Partial preferences, the degree of manipulation, and multi-valuedness”, generalizes the Gibbard-Satterthwaite theorem in three ways: firstly, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; secondly, it is shown that every non-dictatorial surjective social choice function is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; thirdly, we prove a variant of the theorem where the outcomes of the social choice function are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives. The second paper, “Strategy-proof voting for multiple public goods” (coauthored with Lars-Gunnar Svensson), considers a voting model where the set of feasible alternatives is a subset of a product set of finite categories and characterizes the set of all strategy-proof social choice functions for three different types of preference domains over , namely for the three cases when voters’ preferences over are additive, completely separable respectively weakly separable.
- Lars-Gunnar Svensson