In 2011, Brandt proposed a new tournament solution called the minimal extending set (ME). It was conjectured that ME satisfies a large number of desirable properties. In this paper, we non-constructively show that ME fails to satisfy most of these properties. However, no concrete examples of these violations are known and it appears that ME satisfies these properties for all practical purposes. This casts doubt on the axiomatic method.
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Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Chen, Xujin
Ding, Guoli
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Louisiana State Univ, Math Dept, Baton Rouge, LA 70803 USAChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Ding, Guoli
Zang, Wenan
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Univ Hong Kong, Dept Math, Hong Kong, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Zang, Wenan
Zhao, Qiulan
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Nanjing Univ, Dept Math, Nanjing 210093, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
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Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, IsraelTel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel
Alon, N
Brightwell, G
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel
Brightwell, G
Kierstead, HA
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel
Kierstead, HA
Kostochka, AV
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel
Kostochka, AV
Winkler, P
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel