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

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...

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Bibliographic Details
Published in:arXiv.org 2020-11
Main Authors: Bruns, Winfried, Ichim, Bogdan
Format: Article
Language:English
Subjects:
Algorithms
Descent
Polytopes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422