Extension: A theory of discrete hierarchies as optimal cost-adjusted productivity organisations
Scale changes the institutional problem. Lera and Sornette model the coordination cost of a flat organization as approximately proportional to N(N minus 1) divided by 2, the number of pairwise interactions. The cost is therefore quadratic in group size. Their hierarchical model reorganizes those interactions into bounded groups and higher levels that coordinate and control them. This result gives independent support to the scaling mechanism in Kaal's claim, but not to its full legal content. The model concerns human organizations, communication, and control. It does not measure responsibility, remedy, value attribution, security review, or agent integration. It also does not establish that every component arrangement exhibits the same exponent. The practical consequence is narrower. An architecture that leaves each participant to negotiate responsibility and settlement separately exposes the system to a pairwise burden. A common institutional layer changes that topology. It can define shared identity, evidence, allocation, and remedy rules once, then make bilateral exceptions explicit. The core should record which rule governed each outcome and preserve the evidence required to apply it. The remaining claim is empirical. Integration effort, security review, support burden, and user understanding must be measured across deployments, with component count and interface density separated. Until those measurements exist, quadratic coordination theory supports the design direction. It does not establish a production cost estimate.
economicsinstitutional-designai-and-agentsgovernance-designcoordination-costssystems-integrationscalingaccountability