On Ordering a Set of Degressively Proportional Apportionments

Katarzyna Cegiełka , Piotr Dniestrzański , Janusz Łyko , Arkadiusz Maciuk , Radosław Rudek

Abstract

The most important problem in a practical implementation of degressive proportionality is its ambiguity. Therefore, we introduce an order relation on a set of degressively proportional allocations. Its main idea is to define greater allocations such that emerge from other after transferring a certain quantity of goods from smaller to greater entities contending in distribution. Thus, maximal elements in this ordering are indicated as the sought-after solution sanctioning boundary conditions as the only reason of moving away from the fundamental principle of proportionality. In case of several maximal elements the choice of one allocation remains an open issue, but the cardinality of the set from which we make a choice can be reduced significantly. In the best-known example of application of degressive proportionality, which is the apportionment of seats in the European Parliament, the considered set contains a maximal element. Thereby, there exits an allocation that is nearest to the proportional distribution with respect to transfer relation
Author Katarzyna Cegiełka (MISaF / IZM / DoMaC)
Katarzyna Cegiełka,,
- Department of Mathematics and Cybernetics
, Piotr Dniestrzański (MISaF / IZM / DoMaC)
Piotr Dniestrzański,,
- Department of Mathematics and Cybernetics
, Janusz Łyko (MISaF / IZM / DoMaC)
Janusz Łyko,,
- Department of Mathematics and Cybernetics
, Arkadiusz Maciuk (MISaF / IZM / DoMaC)
Arkadiusz Maciuk,,
- Department of Mathematics and Cybernetics
, Radosław Rudek (MISaF / IBI / DIT)
Radosław Rudek,,
- Department of Information Technologies
Journal seriesLNCS Transactions on Computational Collective Intelligence, ISSN 2190-9288, e-ISSN 1611-3349, (B 10 pkt)
Issue year2017
Vol10480
Pages53-62
Publication size in sheets0.5
Keywords in EnglishAllocation Degressive proportionality Transfer order
DOIDOI:10.1007/978-3-319-70647-4_4
URL https://link.springer.com/chapter/10.1007%2F978-3-319-70647-4_4
Languageen angielski
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Score (nominal)10
Score sourcejournalList
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