On the structure of stable tournament solutions
A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show th...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal article |
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Springer
2016
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| _version_ | 1826282371199008768 |
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| author | Brandt, F Brill, M Seedig, H Suksompong, W |
| author2 | Alexander von Humboldt Foundation |
| author_facet | Alexander von Humboldt Foundation Brandt, F Brill, M Seedig, H Suksompong, W |
| author_sort | Brandt, F |
| collection | OXFORD |
| description | A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature. |
| first_indexed | 2024-03-07T00:42:50Z |
| format | Journal article |
| id | oxford-uuid:83a38bfb-7a1a-4215-9e8a-5bc9a59caa98 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:42:50Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:83a38bfb-7a1a-4215-9e8a-5bc9a59caa982022-03-26T21:45:32ZOn the structure of stable tournament solutionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:83a38bfb-7a1a-4215-9e8a-5bc9a59caa98Symplectic Elements at OxfordSpringer2016Brandt, FBrill, MSeedig, HSuksompong, WAlexander von Humboldt FoundationA fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature. |
| spellingShingle | Brandt, F Brill, M Seedig, H Suksompong, W On the structure of stable tournament solutions |
| title | On the structure of stable tournament solutions |
| title_full | On the structure of stable tournament solutions |
| title_fullStr | On the structure of stable tournament solutions |
| title_full_unstemmed | On the structure of stable tournament solutions |
| title_short | On the structure of stable tournament solutions |
| title_sort | on the structure of stable tournament solutions |
| work_keys_str_mv | AT brandtf onthestructureofstabletournamentsolutions AT brillm onthestructureofstabletournamentsolutions AT seedigh onthestructureofstabletournamentsolutions AT suksompongw onthestructureofstabletournamentsolutions |