Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach
In the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their valu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1269 |
| _version_ | 1797525970781995008 |
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| author | Ewa Łyko Janusz Łyko Arkadiusz Maciuk Maciej Szczeciński |
| author_facet | Ewa Łyko Janusz Łyko Arkadiusz Maciuk Maciej Szczeciński |
| author_sort | Ewa Łyko |
| collection | DOAJ |
| description | In the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their values. The division performed according to this principle is ambiguous, and its selection requires many negotiations among participants. The aim of this paper is to limit the range of such negotiations when the problem is complex, i.e., the set of feasible solutions has high cardinality. It can be done thanks to a numerical analysis of the set of all feasible solutions, and eliminating allocations favoring or disfavoring some coalitions of agents. The problem is illustrated by the case study of allocating seats in the European Parliament in its 2019–2024 term. |
| first_indexed | 2024-03-10T09:21:35Z |
| format | Article |
| id | doaj.art-3091faf1d8b540189e0ca986a172dcaa |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T09:21:35Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3091faf1d8b540189e0ca986a172dcaa2023-11-22T05:09:48ZengMDPI AGSymmetry2073-89942021-07-01137126910.3390/sym13071269Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic ApproachEwa Łyko0Janusz Łyko1Arkadiusz Maciuk2Maciej Szczeciński3Faculty of Computer Science and Management, Wroclaw University of Science and Technology, Wyspianski St. 27, 50-370 Wrocław, PolandWroclaw University of Economics and Business, Komandorska St. 118/120, 53-345 Wrocław, PolandWroclaw University of Economics and Business, Komandorska St. 118/120, 53-345 Wrocław, PolandWroclaw University of Economics and Business, Komandorska St. 118/120, 53-345 Wrocław, PolandIn the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their values. The division performed according to this principle is ambiguous, and its selection requires many negotiations among participants. The aim of this paper is to limit the range of such negotiations when the problem is complex, i.e., the set of feasible solutions has high cardinality. It can be done thanks to a numerical analysis of the set of all feasible solutions, and eliminating allocations favoring or disfavoring some coalitions of agents. The problem is illustrated by the case study of allocating seats in the European Parliament in its 2019–2024 term.https://www.mdpi.com/2073-8994/13/7/1269asymmetrizationlexicographic orderfair divisiondegressively proportional allocationEuropean Parliamentsequential coalition |
| spellingShingle | Ewa Łyko Janusz Łyko Arkadiusz Maciuk Maciej Szczeciński Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach Symmetry asymmetrization lexicographic order fair division degressively proportional allocation European Parliament sequential coalition |
| title | Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach |
| title_full | Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach |
| title_fullStr | Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach |
| title_full_unstemmed | Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach |
| title_short | Asymmetrization of a Set of Degressively Proportional Allocations with Respect to Lexicographic Order. An Algorithmic Approach |
| title_sort | asymmetrization of a set of degressively proportional allocations with respect to lexicographic order an algorithmic approach |
| topic | asymmetrization lexicographic order fair division degressively proportional allocation European Parliament sequential coalition |
| url | https://www.mdpi.com/2073-8994/13/7/1269 |
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