Accounting for Coalition Feasibility in Measures of Voting Power

When winning coalitions are implausible

In corporate governance, cartel formation and parliamentary voting, some coalitions may be able to win yet remain implausible because of ideological differences, institutional constraints or pre-electoral agreements. Thomas Pitz and Vinicius Ferraz propose power measures that account for this distinction.

Only the abstract is available for this article. The account below describes the authors’ reported results, not an assessment of the full proofs or applications.

Two approaches to cohesion

The authors introduce “cohesion structures” to quantify coalition feasibility. They report axiomatic characterizations of two families of cohesion-sensitive power indices: mathematical rules for assigning influence to participants. Both are represented as expected marginal contributions under what the abstract calls Luce-type distributions. In accessible terms, influence depends on the difference a participant makes, averaged using specified probabilities.

For the Banzhaf family, coalition weights are a power transformation of cohesion. For the Shapley family, additional axioms separate coalition size from cohesion: classical size weights are retained, while cohesion affects weighting within each size class.

Reported verification and illustrations

The abstract states that all results have been mechanically verified in Lean 4 with Mathlib. It also reports illustrations involving the German Bundestag and French Assemblée Nationale. The authors describe sharp, interpretable shifts in power under cordon sanitaire and double cordon scenarios; the abstract supplies no numerical results.

Version and revision notice

This account concerns 2603.27220v2. The metadata records initial publication on March 28, 2026, and an update on November 5, 2026. Its comment explicitly states: “major restructuring will be done.”