Weak order polytopes Original Research Article

The weak order polytope PWOn is defined as the convex hull in Rn(n−1) of the characteristic vectors of all reflexive weak orders on {1,2,…,n}. The paper focuses on facet-defining inequalities, vertex adjacency and symmetries. We relate PWOn to the theories of probabilistic choice and preference aggregation, prove a basic lifting lemma that carries facet-defining inequalities for PWOn into PWOn+1, identify complete sets of facet-defining inequalities for n⩽4, give a complete account of vertex adjacency, and determine all symmetries of PWOn.