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.
| 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 |

