Date of Publication

12-2022

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with Specialization in Computer Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

John Vincent S. Morales

Defense Panel Chair

Ederlina G. Nocon

Defense Panel Member

Yvette F. Lim

Abstract/Summary

In democratic societies, elections are done to determine rightful candidates to hold public office. In situations where voters are required to rank all the political candidates from most preferred to the least, a scoring rule is used. In an election held under a scoring rule, a candidate receives a score based on their ranking on the voter’s ballot. The highest score
is awarded to the most preferred candidate while the lowest score is given to the least. In this thesis, we view an election held under a scoring rule as a game where the players are the political candidates and the payoffs are the total scores. We will look into the game’s Nash equilibrium – a state in which any candidate does not gain a higher score by changing
his/her strategy while others keep theirs. A Nash equilibrium is classified as convergent (resp.
nonconvergent) whenever players have unanimous (resp. split) strategies in the equilibrium. The aim of this thesis is to contribute to the objective of finding some characterization of scoring rules where non-convergent Nash equilibria (NCNE) exist. Specifically, we focus on a certain type of scoring rule where negative scores are given to the least preferred candidates. For such scoring rules, we shall use the term disapproval voting. In this study, we prove that,
in an m-candidate election with m ≥ 4, the disapproval voting whose scoring rule awards negative points to m − k least preferred candidates for k ≥ ⌊ m 2 ⌋ does not have NCNE.

Abstract Format

html

Language

English

Format

Electronic

Physical Description

22 leaves

Keywords

Voting; Equilibrium; Game theory

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Embargo Period

12-18-2022

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