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Essays in Strategy-proof Social Choice Theory

Reffgen, Alexander LU (2010)
Abstract
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... (More)
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. (Less)
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58 pages
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English
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yes
id
3246766b-995b-4221-9b9c-43db6c956f15 (old id 1714330)
date added to LUP
2010-11-16 14:00:33
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2016-09-19 08:45:17
@misc{3246766b-995b-4221-9b9c-43db6c956f15,
  abstract     = {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.},
  author       = {Reffgen, Alexander},
  language     = {eng},
  pages        = {58},
  title        = {Essays in Strategy-proof Social Choice Theory},
  year         = {2010},
}