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<p>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.&#xa0;Electoral College and the Parliament of Bosnia–Herzegovina.</p>

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Weighted simple games and the topology of simplicial complexes

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Anastasia Brooks,
  • Franjo Šarčević,
  • Ismar Volić

摘要

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.