Mathematical Programming Computation, Volume 13, Issue 2, June 2021

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

Winfried Bruns, Bogdan Ichim

We describe the computation of polytope volumes by descent in the face lattice, its implementation in Normaliz, and the connection to reverse-lexicographic triangulations. The efficiency of the algorithm is demonstrated by several high dimensional polytopes of different characteristics. Finally, we present an application to voting theory where polytope volumes appear as probabilities of certain paradoxa.

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