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A classification of peak-pit maximal Condorcet domains.
- Source :
-
Mathematical Social Sciences . Sep2023, Vol. 125, p42-57. 16p. - Publication Year :
- 2023
-
Abstract
- In this paper, we introduce a weaker notion of separability for set-systems and demonstrate that the class of maximal weakly separated systems precisely corresponds to the class of peak-pit maximal Condorcet domains. Additionally, we present a generalisation of arrangements of pseudolines and establish that the sets of chamber sets from them coincide with maximal weakly separated systems, enabling the construction of all peak-pit maximal Condorcet domains. Furthermore, we reveal that peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains. • Peak-pit maximal Condorcet domains are characterised by weakly separated ideals. • Weakly separated ideals are characterised by generalised arrangements of pseudolines. • Peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains. • Peak-pit maximal Condorcet domains are copious and ample. • The size of the ideal of any peak-pit maximal Condorcet domain on [n] is n + 1 2 + 1. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SOCIAL choice
*PLURALITY voting
*LINEAR orderings
*GENERALIZATION
*CLASSIFICATION
Subjects
Details
- Language :
- English
- ISSN :
- 01654896
- Volume :
- 125
- Database :
- Academic Search Index
- Journal :
- Mathematical Social Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 170412979
- Full Text :
- https://doi.org/10.1016/j.mathsocsci.2023.06.004