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master's thesis
Problem proporcionalne zastupljenosti i cjelobrojna optimizacija
Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Applied Mathematics and Informatics, 2023. urn:nbn:hr:126:596756
Tušek, Marija
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Tušek, M. (2023). Problem proporcionalne zastupljenosti i cjelobrojna optimizacija (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:596756

Tušek, Marija. "Problem proporcionalne zastupljenosti i cjelobrojna optimizacija." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:596756

Tušek, Marija. "Problem proporcionalne zastupljenosti i cjelobrojna optimizacija." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:596756

Tušek, M. (2023). 'Problem proporcionalne zastupljenosti i cjelobrojna optimizacija', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:596756

Tušek M. Problem proporcionalne zastupljenosti i cjelobrojna optimizacija [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:596756

M. Tušek, "Problem proporcionalne zastupljenosti i cjelobrojna optimizacija", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:596756

Metadata
TitleProblem proporcionalne zastupljenosti i cjelobrojna optimizacija
Title (english)Proportional Representation Problem And Integer Optimization
AuthorMarija Tušek
MentorTomislav Marošević (mentor)
Committee memberMihaela Ribičić Penava (predsjednik povjerenstva)
Committee memberTomislav Marošević (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-07-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tradicionalno, proporcionalne alokacijske metode analiziraju se raznim indeksima neproporcionalnosti. Na temelju tih analiza smatra se da metoda najvećih ostataka daje najproporcionalnije rezultate, dok d’Hondtova metoda, koja se koristi i u Hrvatskoj za izbor saborskih zastupnika, često biva kritizirana da daje manje proporcionalne rezultate i pogoduje velikim političkim strankama. Kroz ovaj rad promatramo novi pristup cjelobrojne optimizacije koji sa snažnom matematičkom podlogom, koristeći funkciju cilja, konveksne funkcije i pohlepne algoritme, zapravo otkriva da je tradicionalni pristup analize proporcionalnosti pogrešan. Svaka alokacijska metoda je pohlepni algoritam koji minimizira određenu funkciju cilja koja nije nužno jedinstvena, već ovisi o odabranoj metodi. Stoga, njihova usporedba i rangiranje metoda po kriteriju proporcionalnosti ne daje jednoznačan odgovor. Pristup cjelobrojne optimizacije također omogućuje dizajn novih alokacijskih metoda koje minimiziraju neke nove indekse neproporcionalnosti koji imaju poželjna matematička svojstva.
Abstract (english)
Traditionally, proportional allocation methods are analyzed by various indices of disproportionality. Based on these analyses, it is considered that the method of the largest remainders gives the most proportional results, while the d’Hondt method, which is also used in Croatia for the election of members of parliament, is often criticized for giving less proportional results and favoring large political parties. Through this paper, we observe a new approach to integer optimization that, with a strong mathematical foundation, using the objective function, convex functions and greedy algorithms, actually reveals that the traditional proportionality analysis approach is wrong. Each allocation method is a greedy algorithm that minimizes a certain objective function that is not necessarily unique, but depends on the chosen method. Therefore, their comparison and ranking of methods according to the criterion of disproportionality does not give an unequivocal answer. The integer optimization approach also enables the design of new allocation methods that minimize some new disproportionality indices that have desirable mathematical properties.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:596756
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-07-19 09:38:02