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 present an application to voting theory where polytope volumes appear as probabilities of certain paradoxa.

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Metadaten
Author:Winfried Bruns, Bogdan Ichim
DOI:https://doi.org/10.1007/s12532-020-00198-z
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2020
Tag:Software; Theoretical Computer Science
Volume:13
Issue:2
Page Number:28
First Page:415
Last Page:442
Mathematical Programming Computation :MPC 2021 - Issue 2
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