Surface volumes of rounding polytopes

Mathias Drton*, Udo Schwingenschlögl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The paper determines the vertices and surface volumes of all rounding polytopes for commonly used rounding methods: The quota method of greatest remainders, and the divisor methods. These methods are used to round continuous non-negative weights summing to one to non-negative integers summing to a predetermined accuracy, e.g. to 100 when rounding to percentages. Our results are of interest when average properties of rounding methods are investigated, and an example from political science is included.

Original languageEnglish (US)
Pages (from-to)71-91
Number of pages21
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - Feb 1 2004
Externally publishedYes


  • Apportionment method
  • Probability simplex
  • Proportional representation
  • Rounding method
  • Rounding rule
  • Seat allocation
  • Seat bias

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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