Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems
- When the seats in a parliamentary body are to be allocated proportionally to some given weights, such as vote counts or population data, divisor methods form a prime class to carry out the apportionment. We present a new characterization of divisor methods, via primal and dual optimization problems. The primal goal function is a cumulative product of the discontinuity points of the rounding rule. The variables of the dual problem are the multipliers used to scale the weights before they get rounded. Our approach embraces pervious and impervious divisor methods, and vector and matrix problems.
| Author: | Norbert GaffkeGND, Friedrich PukelsheimGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4164 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/515 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-05) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2007/05/30 |
| Tag: | apportionment method; optimization problem; divisor method; proportional representation system |
| GND-Keyword: | Wahlverfahren; Verhältniswahl; Optimierungsproblem; Divisionsalgebra; Verteilungsfunktion |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
