Essays on Strategy-proof Social Choice

Sammanfattning: This thesis makes a contribution to strategy-proof social choice theory, in which one investigates the conditions under which it is possible to construct social choice functions (i.e., voting procedures) that can never be manipulated in the sense that some voter, by misrepresentation of his true preferences, can change the outcome of a voting and obtain an alternative he prefers to the one that honest voting would give. The thesis consists of three separate essays, which provide complete characterizations of the strategy-proof social choice functions in different formal frameworks as described in the following. The first essay, “Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness”, has its starting point in the Gibbard-Satterthwaite theorem, which is the fundamental result of strategy-proof social choice theory. This result states that if exactly one alternative should be elected from a set of at least three eligible alternatives, then a social choice function is strategy-proof if and only if it is dictatorial. This result is generalized in three ways: First, we prove that the theorem is still valid when individual preferences belong to a convenient class of partial preferences. Second, we show that that every non-dictatorial surjective social choice function is not only manipulable, but can be manipulated in such a way that some individual obtains either his best or second best alternative. Third, 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 the second essay, “Strategy-proof voting for multiple public goods” (co-authored with Lars-Gunnar Svensson), we consider a voting model where the set of feasible alternatives is a subset of a product set of several finite categories, and we characterize the set of all strategy-proof social choice functions for three different types of preference domains over the product set, namely for the domains of additive, completely separable, and weakly separable preferences. The third essay, “Strategy-proof social choice on multiple single-peaked domains and preferences for parties”, starts from the concept of single-peaked domains, which play an important role in strategy-proof social choice theory because they admit a large class of non-dictatorial strategy-proof social choice functions. These domains are generalized to multiple single-peaked domains, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be single-peaked. The main result in this essay provides a complete characterization of the strategy-proof social choice functions on multiple single-peaked domains. We show also in the framework of a spatial voting model for party elections that multiple single-peaked domains are appropriate to represent preferences over parties.