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Optimal proportional representation
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5907-0087
2020 (English)Report (Other academic)
Abstract [en]

In a democratic proportional election system, it is vital that the mandates in the parliament are allocated as proportionally as possible to the number of votes the parties got in the election. We formulate an optimization model for allocation of seats in a parliament so as to minimize the disproportionality. By applying separable programming techniques, we obtain an easily solvable problem, and present a method for solving it optimally. The obtained solution is the feasible solution that has the minimal disproportionality (with the measure chosen), even in the presence of a parliament threshold, which is not always the case for the practical procedures used in many countries. We apply the approach to real life data from the last three elections in Sweden, and show that the result is better, i.e. more proportional, than what was obtained with the modified Sainte-Laguë method, which is presently used. A natural suggestion would be to use our method instead.

We also consider the issue about constituencies, and suggest a procedure, based on the same kind of optimization problem, for allocating mandates in the constituencies, without changing the overall allocation with respect to parties. The numbers of mandates for the constituencies are based on the number of votes given, not on estimated numbers of inhabitants entitled to vote. This removes the need for compensatory mandates, and makes the question about sizes of the constituencies less important.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2020.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2020:3
Keywords [en]
OR in government; democracy; proportional representation; Gallagher index; Sainte-Laguë index
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-164134ISRN: LiTH-MAT-R--2020/03--SEOAI: oai:DiVA.org:liu-164134DiVA, id: diva2:1412569
Available from: 2020-03-06 Created: 2020-03-06 Last updated: 2020-03-12Bibliographically approved

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Holmberg, Kaj

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf