Probabilities of majority and minority violation in proportional representation

Udo Schwingenschlögl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Apportionment methods are used in proportional representation systems for rounding electoral vote proportions to integer numbers of seats in parliament. Many criteria are known to judge this adjustment process and to decide whether a specific method is suitable for practical use. As in general it is not possible to fulfill all desired criteria together, it is necessary to consider probabilities of violated criteria for specific apportionment methods. This paper demonstrates how to calculate the probability of such violations for the important majority and minority criteria by means of a recently developed geometric-combinatorial approach. Results are given for several popular apportionment methods.

Original languageEnglish (US)
Pages (from-to)1690-1695
Number of pages6
JournalStatistics and Probability Letters
Issue number17
StatePublished - Nov 2007
Externally publishedYes


  • Apportionment method
  • Geometric-combinatorial approach
  • Hamilton method
  • Majority criterion
  • Minority criterion
  • Stationary divisor methods

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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