English

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