Counter-intuitive result.

The Schelling simulation we just built is a beautiful counterexample to the apriorist approach (code in the comments).
The setup is almost trivially simple: agents on a grid, each willing to live with neighbors of either color as long as some minimum fraction match their own. At a tolerance of just one-third, where every agent would happily accept being outnumbered two-to-one by the other color, you might guess that the equilibrium would look essentially random.
It does not. The simulation shows that even this mild preference produces sharply segregated clusters across the entire grid, with a segregation index near 0.75. At tolerance one-half, segregation reaches 0.87, far beyond what any individual agent demands. The macroscopic outcome looks nothing like the microscopic preference. No one in the simulation wants segregation.
Everyone produces it.
This is the kind of result that pure deduction from an "action axiom" simply cannot deliver.
You can stare at the rule "agents prefer to have at least one-third of their neighbors match their color" for a thousand years and never derive, by reflection alone, that it generates clustering with a sharp phase transition near tolerance 0.3, mean cluster size growing while cluster count shrinks, and dynamics that match the coarsening behavior of physical systems undergoing phase separation. You have to run it.
The world had to be measured. And the measurement revealed something the armchair could not.
This is what real mathematical social science (or economy) looks like, and it is exactly what praxeology refuses to do.