Manipulacije u izbornim sustavima

master's thesis

• Title (english): Manipulations in electoral systems
• Author: Ivan Bartak
• Mentor: Ilko Vrankić (mentor)
• Committee member: Ilko Vrankić (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu bavili smo se manipulacijama u izbornim sustavima u kontekstu ordinalnih preferencija. Uveli smo pojmove glasačkog listića i izbornog profila pomoću binarne relacije, te smo defnirali različite vrste procedura za određivanje ishoda izbora. Zatim smo defnirali dvadeset izbornih pravila i dokazali Arrowljev teorem nemogućnosti transformiranja pojedinačnih preferencija u društvene. Promatrali smo i na koje načine glasač može manipulirati izborno pravilo, te smo za neka pravila dali konkretne primjere kada je to moguće ili nije. Dokazali smo Gibbard-Satterthwaiteov teorem za rezolutna izborna pravila koji tvrdi da je diktatura jedino rezolutno pravilo koje nije manipulabilno i zadovoljava Paretovo svojstvo, te smo dokazali ekvivalenciju Gibbard-Satterthwaiteovog i Arrowljevog teorema. Zatim smo za nerezolutna pravila dokazali Duggan-Schwartzov, Feldmanov i Gaerdenforsov teorem, koji uz određene izmjene pretpostavki, poopćavaju Gibbard-Satterthwaiteov teorem.

Abstract (english)

In this thesis we dealt with manipulations in voting systems. We introduced the terms of ballot and election profile with a help of binary relations, also we defined different types of aggregate procedures for determining the outcome of elections. Then we defined twenty voting rules and proved Arrow's theorem of impossibility of transforming individual preferences into social preferences. We also looked at possible ways in which voter could manipulate the voting rule, and for some rules we have given concrete examples of when it is possible and when it isn't. We proved the Gibbard-Satterthwaite's theorem for resolute voting rules which claims that dictatorship is the only resolute rule that is not manipulable and satisfies Pareto's condition, and we have proved the equivalency of Gibbard-Satterthwaite's and Arrow's theorems. Then, for non-resolute rules, we proved Duggan-Schwartz's, Feldman's and Gaerdenfors's theorem which, with some changes in the assumptions, generalizes Gibbard-Satterthwaite's theorem.

• Keywords: Arrowljev teorem nemogućnosti; Gibbard-Satterthwaiteov teorem; Paretovo svojstvo
• Keywords (english): Arrow's theorem of impossibility; Gibbard-Satterthwaite's theorem; Pareto's condition
• Language: croatian
• URN:NBN: urn:nbn:hr:217:003512
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-25 08:58:27