Izborni sustavi i proporcionalnost

master's thesis

• Author: Ana Alagić
• Mentor: Damir Bakić (mentor)
• Committee member: Damir Bakić (predsjednik povjerenstva)
• Committee member: Luka Grubišić (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Zlatko Drmač (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome radu se bavimo metodama razdiobe mandata na temelju broja glasova u proprcionalnim izbornim sustavima. U prvom poglavlju, opisujemo nekoliko metoda poput D’Hontove, Sainte-Lagueove, Jeffersonove i Websterove metode. Zatim pokazuje da su D’Hondtova i Jeffersonova metoda ekvivalentne, kao i Sainte-Lagueove i Websterova. U drugom poglavlju naglasak je na D’Hondtovoj metodi. Pokazujemo da teži proporcionalnoj raspodjeli mjesta u predstavničkom tijelu, odnosno, kada veličina predstavničkog tijela teži ka beskonačnosti, tada udio pojedine liste u mandatima teži udjelu te liste u glasovima. U slučaju manjeg predstavničkog tijela, blagu prednost daje vodećim listama. Jamči da dobitnik natpolovične većine glasova dobije i natpolovičnu većinu mjesta. Na simulacijama se vidi da koaliranje neće puno utjecati na rezultate izbora. No, ipak postoji vjerojatnost da koaliranje promijeni ishod u slučaju kada dva bloka imaju približno isti broj glasova. U trećem poglavlju bavimo se općom teorijom razdiobe mandata. Navodimo nekoliko poznatih paradoksa koji su se dogodili kroz povijest. Pokazujemo da su djeliteljske metode populacijski monotone zbog čega su popularne u tradicionalnim pristupima. Djeliteljske metode neće dovesti do “paradoksa Alabame.” Ne postoji djeliteljska metoda koja poštuje “pravilo kvote” za svaki problem.

Abstract (english)

In this paper, we deal with methods of distribution of seats based on the number of votes in proportional electoral systems. In the first chapter, we describe several methods such as D’Hont’s, Sainte-Lague’s, Jefferson’s and Webster’s methods. In the second chapter, the emphasis is on D’Hondt’s method. We show that it tends to the proportional distribution of seats in the representative body, that is, when the size of the representative body tends to infinity, then the share of an individual list in the mandates tends to the share of that list in the votes. In the case of a smaller representative body, it gives a slight advantage to the leading lists. It guarantees that the winner of more than half of the votes also receives more than half of the seats. The simulations show that the coalition will not have much of an impact on the election results. However, there is a possibility that the coalition will change the outcome in the case when two blocs have approximately the same number of votes. In the third chapter, we deal with the general theory of the distribution of mandates. Here are a few well-known paradoxes that have occurred throughout history. We show that divisor methods are population monotone which is why they are popular in traditional approaches. Divisor methods will not lead to the “Alabama paradox.” There is no divisor method that follows the “quota rule” for every problem.

• Keywords: metode razdiobe mandata; D’Hontova; Sainte-Lagueova: Jeffersonova; Websterova metoda
• Keywords (english): proportional electoral systems; methods of distribution; D’Hont’s; Sainte-Lague’s; Jefferson’s; Webster’s method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:871177
• Study programme: Title: Applied 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: 2020-12-07 11:34:57