Surface volumes of rounding polytopes

Mathias Drton; Udo Schwingenschlögl

doi:10.1016/j.laa.2003.09.005

Surface volumes of rounding polytopes

Mathias Drton^*, Udo Schwingenschlögl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	71-91
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	378
Issue number	1-3
DOIs	https://doi.org/10.1016/j.laa.2003.09.005
State	Published - Feb 1 2004
Externally published	Yes

Keywords

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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10.1016/j.laa.2003.09.005

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abstract = "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.",

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AU - Schwingenschlögl, Udo

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AB - 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.

KW - Apportionment method

KW - Probability simplex

KW - Proportional representation

KW - Rounding method

KW - Rounding rule

KW - Seat allocation

KW - Seat bias

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JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Surface volumes of rounding polytopes

Abstract

Keywords

ASJC Scopus subject areas

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