Scaling Laws of Collective Decision Quality under Different Governance Structures: A Computational Analysis with Empirical Calibration

How does collective decision quality scale with group size under different governance structures? We develop a computational model in which $N$ agents with normally distributed abilities make collective decisions through one of five governance systems---monarchy, aristocracy, direct democracy, indirect democracy, or feudal hierarchy. Each system aggregates individual abilities differently, and a process quality function, calibrated against empirical data on group process losses (Ringelmann 1913; Ingham et al.\ 1974; Mao et al.\ 2016), captures coordination costs that increase logarithmically with the number of active decision-makers. Our central finding is a \emph{governance crossover}: the structure maximizing collective decision quality shifts systematically from direct democracy ($N < 15$) through indirect democracy ($15 \leq N < 75$) and aristocracy ($75 \leq N < 150$) to monarchy ($N \geq 150$) as group size increases. This crossover is robust to the functional form of the cost function (logarithmic, power-law, or square-root). We extend the model to a four-layer feudal hierarchy, showing that it trades information efficiency for corruption resilience: at 50\% corruption, monarchy loses 14\% of its decision quality while the feudal structure loses only 2\%. A dynamic generational model incorporating aging, mortality, education, and selection pressure confirms that the crossover pattern is preserved under demographic turnover. Analytical predictions based on order statistics agree with Monte Carlo simulations within 2\%. All code is available at https://doi.org/10.5281/zenodo.XXXXXXX