Essays on Strategyproof Social Choice
Research output: Thesis › Doctoral Thesis (compilation)
Abstract
This thesis makes a contribution to strategyproof 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 strategyproof social choice functions in different formal frameworks as described in the following.
The first essay, “Generalizing the GibbardSatterthwaite theorem: partial preferences, the degree of manipulation, and multivaluedness”, has its starting point in the GibbardSatterthwaite theorem, which is the fundamental result of strategyproof 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 strategyproof 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 nondictatorial 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, “Strategyproof voting for multiple public goods” (coauthored with LarsGunnar 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 strategyproof 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, “Strategyproof social choice on multiple singlepeaked domains and preferences for parties”, starts from the concept of singlepeaked domains, which play an important role in strategyproof social choice theory because they admit a large class of nondictatorial strategyproof social choice functions. These domains are generalized to multiple singlepeaked domains, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be singlepeaked. The main result in this essay provides a complete characterization of the strategyproof social choice functions on multiple singlepeaked domains. We show also in the framework of a spatial voting model for party elections that multiple singlepeaked domains are appropriate to represent preferences over parties.
The first essay, “Generalizing the GibbardSatterthwaite theorem: partial preferences, the degree of manipulation, and multivaluedness”, has its starting point in the GibbardSatterthwaite theorem, which is the fundamental result of strategyproof 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 strategyproof 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 nondictatorial 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, “Strategyproof voting for multiple public goods” (coauthored with LarsGunnar 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 strategyproof 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, “Strategyproof social choice on multiple singlepeaked domains and preferences for parties”, starts from the concept of singlepeaked domains, which play an important role in strategyproof social choice theory because they admit a large class of nondictatorial strategyproof social choice functions. These domains are generalized to multiple singlepeaked domains, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be singlepeaked. The main result in this essay provides a complete characterization of the strategyproof social choice functions on multiple singlepeaked domains. We show also in the framework of a spatial voting model for party elections that multiple singlepeaked domains are appropriate to represent preferences over parties.
Details
Authors  

Organisations  
Research areas and keywords  Subject classification (UKÄ) – MANDATORY
Keywords

Original language  English 

Qualification  Doctor 
Awarding Institution  
Supervisors/Assistant supervisor 

Award date  2011 Jun 6 
Publication status  Published  2011 
Publication category  Research 
Bibliographic note
Defence details
Date: 20110606
Time: 14:15
Place: Holger Crafoords Ekonomicentrum, Sal EC3:211
External reviewer(s)
Name: Weymark, John
Title: [unknown]
Affiliation: Vanderbilt University
