Thomas Pitz

Thomas Pitz, Vinicius Ferraz

In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral agreements may render certain coalitions implausible. Classical power indices ignore this and weight all winning coalitions equally. We introduce cohesion structures to quantify coalition feasibility and axiomatically characterize two families of cohesion-sensitive power indices, represented as expected marginal contributions under Luce-type distributions. In the Banzhaf branch, coalition weights are a power transformation of cohesion; in the Shapley branch, additional axioms separate size from cohesion, recovering the classical size weights with cohesion acting within each size class. All results have been mechanically verified in Lean 4 with Mathlib. We illustrate the framework on the German Bundestag and the French Assemblée Nationale, where cordon sanitaire and double cordon scenarios produce sharp, interpretable power shifts.

Thomas Pitz, Vinícius Ferraz

Strategic crisis analysis needs representations that combine qualitative expert judgement, explicit interdependence, and auditable update rules without requiring fully specified payoffs or probabilities. Scenario Bundle Analysis (SBA), developed by Amos Perlmutter and Reinhard Selten, provides such a starting point, but the original formulation leaves several database, topology, and update interfaces implicit. This paper presents a formal refinement and extension of the original SBA framework, introducing a two-layer architecture that separates a static scenario database from a dynamic scenario tree system. The extended framework incorporates a richer attitude vocabulary: beliefs, desires, intentions, fears, and coalitional commitments, with expectations treated as doxastic attitudes. It also adds a domain/modifier layer for contextual framing, a topology on admissible scenario spaces\index{Scenario space}, typed assessment-state updates, and multi-criteria evaluation. Mathematical definitions are stated with sufficient precision to support computational implementation.