On the likelihood of single-peaked preferences
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper...
| Autor principal: | |
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| Formato: | Journal article |
| Publicado em: |
Springer Berlin Heidelberg
2017
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| _version_ | 1826274507102355456 |
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| author | Lackner, M Lackner, M |
| author_facet | Lackner, M Lackner, M |
| author_sort | Lackner, M |
| collection | OXFORD |
| description | This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper bound implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption. For single-peaked elections, this upper bound can be refined and complemented by a lower bound that is asymptotically tight. In addition, we provide exact results for elections with few voters or candidates. Moreover, we consider the Pólya urn model and the Mallows model and obtain lower bounds showing that single-peakedness is considerably more likely to appear for certain parameterizations. |
| first_indexed | 2024-03-06T22:44:28Z |
| format | Journal article |
| id | oxford-uuid:5cae23b7-f433-4414-840b-a4feb7ceb018 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:44:28Z |
| publishDate | 2017 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | oxford-uuid:5cae23b7-f433-4414-840b-a4feb7ceb0182022-03-26T17:29:44ZOn the likelihood of single-peaked preferencesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5cae23b7-f433-4414-840b-a4feb7ceb018Symplectic Elements at OxfordSpringer Berlin Heidelberg2017Lackner, MLackner, MThis paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper bound implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption. For single-peaked elections, this upper bound can be refined and complemented by a lower bound that is asymptotically tight. In addition, we provide exact results for elections with few voters or candidates. Moreover, we consider the Pólya urn model and the Mallows model and obtain lower bounds showing that single-peakedness is considerably more likely to appear for certain parameterizations. |
| spellingShingle | Lackner, M Lackner, M On the likelihood of single-peaked preferences |
| title | On the likelihood of single-peaked preferences |
| title_full | On the likelihood of single-peaked preferences |
| title_fullStr | On the likelihood of single-peaked preferences |
| title_full_unstemmed | On the likelihood of single-peaked preferences |
| title_short | On the likelihood of single-peaked preferences |
| title_sort | on the likelihood of single peaked preferences |
| work_keys_str_mv | AT lacknerm onthelikelihoodofsinglepeakedpreferences AT lacknerm onthelikelihoodofsinglepeakedpreferences |