Note on axiomatic properties of apportionment methods for proportional representation systems

Apportionment methods are used in proportional representation systems for the apportionment of parliamentary seats among political parties proportionately to their vote counts, or for the allocation of parliamentary seats between geographical districts proportionately to their population figures. Fr...

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Bibliographic Details
Published in:Mathematical programming 2024, Vol.203 (1-2), p.169-185
Main Authors: Palomares, Antonio, Pukelsheim, Friedrich, Ramírez, Victoriano
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Political parties
Principles
Representations
Theoretical
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Summary:Apportionment methods are used in proportional representation systems for the apportionment of parliamentary seats among political parties proportionately to their vote counts, or for the allocation of parliamentary seats between geographical districts proportionately to their population figures. From an axiomatic viewpoint apportionment methods ought to satisfy six basic principles: anonymity, balancedness, concordance, decency, exactness, and fairness. It is well-known that the first two principles are implied by the last four. In this note it is shown that the last four principles are logically independent of each other.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-022-01835-2