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We will study manipulation in election systems, looking specifically at random manipulation, and basing our work on the results of Friedgut, Kalai, and Nisan and by Xia and Conitzer. We will analyze these results and improve upon them by generalizing the results of Friedgut, Kalai, and Nisan, and loosening the conditions of Xia and Conitzer. These authors condition their results on voting rules having certain properties, and we intend to look at what happens when these conditions are replaced by stronger or weaker conditions. We would also like to tighten the bounds given by these two papers by a constant factor or by making them depend on the number of candidates.
- 2012-03-01 - Proposal
- 2012-04-01 - Preliminary results
- 2013-05-01 - Final results
- 2013-08-01 - Thesis draft
- 2014-01-01 - Thesis
- 2014-04-30 - Defense
- Introduction
- Importance
- Difficulty
- Independent Work
- Proof Summary
- Structure of the Remaining Chapters
- Preliminaries
- Definitions
- Background
- Brief History of Social Choice Theory
- History of Manipulation
- Related Work
- Results
- Lattice Theory
- Main Theorem
- Generalized Lemma 6 of Friedgut
- Generalized Lemma 7 of Friedgut
- Generalized Lemma 8 of Friedgut
- Finished Step 3 of Friedgut
- Main Theorem of Friedgut
- Conclusion
- Open Problems
Friedgut, Kalai, and Nisan have proved that social choice functions can be successfully manipulated by random preference reordering with non-negligible probability. However, their results require two restrictions: the social choice function must be neutral, and the election must have at most 3 alternatives. In this thesis we focus on removing the later restriction and generalizing the results to elections with any number of candidates. We also provide a survey of related work analyzing and comparing results from a number of authors.