Facets of linear signed order polytopes

✍ Scribed by Samuel Fiorini; Peter Fishburn

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 225 KB
• Volume: 131
• Category: Article
• ISSN: 0166-218X
• DOI: 10.1016/s0166-218x(03)00224-5

✦ Synopsis

Self-re ecting signed orders have been proposed to aid assessment of preferences between subsets of an n-item set {1; 2; : : : ; n} by considering desirabilities of excluding as well as including items in a set. A linear signed order for n is a linear order on the 2n-element set {1; : : : ; n} ∪ {1 * ; : : : ; n * }, where (x * ) * = x, which satisÿes the self-re ection property x y ⇔ y * x * . The linear signed order polytope Qn for n is deÿned in a standard way as a polytope in [0; 1] 2n(2n-1) . It has dimension n 2 . We note a complete equation system for Qn and specify all facet deÿning inequalities for n 6 4. Additional classes of facets for larger n that are not induced by a lifting lemma are identiÿed. Comparisons to linear ordering polytopes are included.