A Social Spin Foam Model for Power Analysis and Governance Decision-Making

Governance addresses social facts that are heterogeneous in kind, relational in constitution, event-laden, and observed only in part. A state vector, a network, or a single causal model represents some of these features and not the others together. This paper develops a representation in which social facts of any type are carried by the faces of a two-complex, couplings between them are carried by edges, and joint compatibility among several coupled facts is carried by vertices, so that ontological type is independent of geometric dimension and higher-order structure, including relations among relations, is expressible without special provision. Admissibility of a coupling is shown to be the support of a non-negative edge weight, which unifies the type discipline with the weighting. Weights over histories of such structures are then defined, with configuration weights and single-fact weights obtained by marginalisation, and a criterion is given for when alternative histories compose additively, namely the presence of a record that distinguishes them. Reconstruction of structure from observation is posed as a penalised inverse problem whose output is an ensemble of weighted candidates in place of one reconstructed reality, and a minimal case with five observed facts exhibits the reconstruction of unobserved structure from divergent outcomes among closely matched cases. Power is then defined as the capacity to redistribute weight over the space of possible configurations, measured by a divergence between distributions rather than by a difference of weights, and the three received faces of power are recovered as variation at three levels of the model: labels, admissibility, and the type system itself. Governance is distinguished from power as its organised, institutionalised and accountable exercise. Decision is treated as multi-objective search over admissible configurations, returning a set of non-dominated candidates and declining to reduce them to one. The contribution is a representation adequate to heterogeneous relational facts, a definition of power as an invariant of weight redistribution, and a decision procedure that separates what computation settles from what it cannot.