In many practical situations, indifference is intransitive. This led Luce (1956) to base a prefer... more In many practical situations, indifference is intransitive. This led Luce (1956) to base a preference model on the following principle: an alternative is judged better than another one only if the utility value of the first alternative is significantly higher than the value of the second alternative. Here, 'significantly higher' means higher than the value augmented by some constant threshold.
ABSTRACT The $m$-subspace polytope is defined as the convex hull of the characteristic vectors of... more ABSTRACT The $m$-subspace polytope is defined as the convex hull of the characteristic vectors of all $m$-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general $m$-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the $m$-subspace polytope is completely described and the adjacency of vertices is fully characterized.
In many practical situations, indifference is intransitive. This led Luce (1956) to base a prefer... more In many practical situations, indifference is intransitive. This led Luce (1956) to base a preference model on the following principle: an alternative is judged better than another one only if the utility value of the first alternative is significantly higher than the value of the second alternative. Here, 'significantly higher' means higher than the value augmented by some constant threshold.
ABSTRACT The $m$-subspace polytope is defined as the convex hull of the characteristic vectors of... more ABSTRACT The $m$-subspace polytope is defined as the convex hull of the characteristic vectors of all $m$-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general $m$-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the $m$-subspace polytope is completely described and the adjacency of vertices is fully characterized.
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