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We describe the computation of polytope volumes by descent in the facelattice, its implementation in Normaliz, and the connection toreverse-lexicographic triangulations. The efficiency of the algorithm isdemonstrated by several high dimensional polytopes of differentcharacteristics. Finally, we present an application to voting theory wherepolytope volumes appear as probabilities of certain paradoxa.

Polytope volume by descent in the face lattice and applications in social choice