Weighted simple games and the topology of simplicial complexes
Physics and Society
2025-08-29 v3 Combinatorics
Abstract
We use simplicial complexes to model simple games as well as weighted voting games where certain coalitions are considered impossible. Topological characterizations of various ideas from simple games are provided, as are the expressions for Banzhaf and Shapley-Shubik power indices for weighted games. We calculate the indices in several examples of weighted voting games with unfeasible coalitions, including the U.S. Electoral College and the Parliament of Bosnia-Herzegovina.
Keywords
Cite
@article{arxiv.2210.09771,
title = {Weighted simple games and the topology of simplicial complexes},
author = {Anastasia Brooks and Franjo Sarcevic and Ismar Volic},
journal= {arXiv preprint arXiv:2210.09771},
year = {2025}
}
Comments
27 pages, 5 figures, 4 tables