Computational Considerations Of Voting Rules (παιγνιοθεωρητική Ανάλυση Συστημάτων Ψηφοφορίας)

Abstract

In this thesis we are examining various results in the field of Voting seen as a subfield ofmechanism design. The fact that Voting lies on the interface of computer science, operationsresearch and political science seems of particular interest to us. In the introduction a generaldescription of the field of mechanism design and game theory is given. Next is considered thetraditional track of study, i.e. the direction of research before computational considerationswere introduced. We stress out the importance of the Gibbart-Satterthwaite theorem onthe field of Social Choice also in the sense that it gave rise to a new direction of research:studying Social Choice with computational terms. The main focus of the thesis is put on thisdirection of research. Tasks such as winner determination, manipulation, bribery and controlof different voting rules are examined from this point of view. We present results concerningalgorithmic issues, worst-case computational complexity analysis and see what steps havebeen taken towards the average-case complexity analysis, which was really the researchers’desired measure of analysis from the beginning. The focus is put heavily on the problem ofmanipulation.We hope that this thesis will serve as a starting point for other people who want to studythe field.