ArXiv Preprint Defines Three Quantitative Indices for Consultation Breadth and Equality in Group Decisions

The framework records consultations per decision and per member to compute participation indices whose equality is shown through direct algebraic proof. A third index tracks the share of decisions meeting a minimum consultation threshold. Consultation distributions are modeled via discrete maximum-entropy methods from statistical physics, with tail probabilities supplying bounds on the primary index. Survey observations from the two groups align with binomial and Poisson predictions for full-member consultation events. Lorenz curves and Gini coefficients quantify inequality, while a normalized Shannon measure captures participation evenness. Bipartite network representations and controlled simulations demonstrate that identical aggregate consultation levels can mask markedly different member-level distributions.

This sociophysics approach directly quantifies one observable facet of internal democracy, with immediate relevance to corporate boards, legislative committees, and online governance where consultation logs exist. It extends prior work on maximum-entropy models in social systems by adding explicit equality proofs and network visualizations that reveal hidden concentration of influence. Unlike purely qualitative assessments, the indices permit statistical comparison across organizations and time.

The main limitation is reliance on only two aggregate datasets without individual-level validation or longitudinal tracking. Replication on larger, time-stamped consultation records from multiple organizations would strengthen causal claims about how index values predict decision acceptance or group stability. Future controlled experiments that vary meeting protocols could test whether shifts in the indices precede measurable changes in member satisfaction.