A neutral core of degressively proportional allocations under lexicographic preferences of agents

Katarzyna Cegiełka (), Piotr Dniestrzański (), Janusz Łyko (), Arkadiusz Maciuk () and Maciej Szczeciński ()
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Katarzyna Cegiełka: Wroclaw University of Economics and Business
Piotr Dniestrzański: Wroclaw University of Economics and Business
Janusz Łyko: Wroclaw University of Economics and Business
Arkadiusz Maciuk: Wroclaw University of Economics and Business
Maciej Szczeciński: Wroclaw University of Economics and Business

Eurasian Economic Review, 2021, vol. 11, issue 4, No 5, 667-685

Abstract: Abstract One of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

Keywords: Fair division; Lexicographic order; Degressive proportionality; European Parliament (search for similar items in EconPapers)
JEL-codes: D30 D63 D69 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s40822-021-00174-5

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