Pan, Chenxin (2021) Optimal voting order under sequential voting schemes. PhD thesis, University of Warwick.

PDF WRAP_Theses_Pan_2021.pdf - Submitted Version Embargoed item. Restricted access to Repository staff only until 31 August 2023. Contact author directly, specifying your specific needs. - Requires a PDF viewer. Download (6Mb)

Request Changes to record.

Abstract

Voting theory is a branch of social choice theory, which studies the process and pro- cedures of the collective decision. Social choice theory aims to capture the features of transformation from individual judgements to collective judgements using applied math- ematics. These studies are not limited to analysing cases such as legislation committees, expert panels and boards, but also summarising general approaches and models using mathematical modelling and proofs. Social choice theory impacts many subjects, such as political science, economics, applied mathematics, sociology, and even computer science. In addition to helping to comprehend the process of collective decision-making, these results and models can be applied to designing organisational structures and mecha- nisms of social welfare. This study focuses on one particular aspect of collective decision making: the optimal voting order under generalised sequential voting schemes.

The origin of this research goes as far back as the Condorcet Jury Theorem (CJT) (Con- dorcet 1785). In the CJT model, a jury needs to decide between two alternative states of nature, saying A \guilty" or B \innocent" in a legal trial. The theorem states that if the jurors are competent (better than random but worse than perfect), the probability of a correct by majority rule is higher than that of each individual juror, and this probability will converge to one when the number of jurors approaches infinity. The results of the CJT are cited in the works of political science to show the advantages of the democratic system. However, the idealistic assumptions of the CJT, especially requiring homoge- neous competence and independence among jurors, should not be neglected. Although there is a large body of literature on the extensions through relaxing the assumptions about CJT (see Section 1.1.2), CJT under sequential voting schemes still lacks attention beyond works of Dekel & Piccione (2000), Sorensen & Ottaviani (2001), and Alpern & Chen (2017a,b). When jurors' abilities are homogeneous in classic CJT, the voting order makes no difference to the verdict. Under the sequential voting scheme with heteroge- neous abilities, the voting order is of significance as the voters need to know the ascribed votes of two states (number of votes for states A and B) and the votes' composition (how individual jurors voted). Thus, the voting sequences concerning jurors' abilities significantly impact the probability of the correct verdict in sequential voting schemes.

Item Type:	Thesis (PhD)
Subjects:	H Social Sciences > HM Sociology J Political Science > JF Political institutions (General)
Library of Congress Subject Headings (LCSH):	Voting -- Mathematical models, Jurors -- Mathematical models, Rational choice theory, Group decision making, Game theory
Official Date:	August 2021
Dates:	Date Event August 2021 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Warwick Business School
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Chen, Bo ; Alpern, Steve, 1948-
Format of File:	pdf
Extent:	iv, 130 leaves : illustrations
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item