A Shared Threshold Rule for Ants and Workers: Multi-Objective Design of Labour-Force Participation Policy and a Division-of-Labour Evolutionary Algorithm

Tax-benefit policy acts most directly on whether adults work. We show that the response-threshold rule by which social insects divide labour and the extensive-margin participation curve share one functional form when the private cost of working is additive and log-logistic; an assumed participation elasticity then implies the exponent. The correspondence defines a tax-benefit design problem with three objectives—participation, welfare and fiscal cost–whose exact supported Pareto front we compute, and an eleven-instrument version for single adults and lone parents. It also drives MOEA/D-DoL, a decomposition-based algorithm whose subproblems are served by threshold-driven workers that compare their success with the colony’s. By IGD, MOEA/D-DoL beats its MOEA/D-DE core clearly on two of seventeen benchmarks, both used in its design, and on two of nine held-out WFG problems, losing on one benchmark; AR-MOEA, NSGA-III and NSGA-II rank higher on both suites. The schedules that raise participation most at no extra cost lower the guaranteed income and pay an in-work credit financed by a higher tax rate. This direction survives joint calibration draws, a 100% cap on marginal rates and wider instrument ranges, but the tax is cheap partly because hours do not respond, and the gain varies in size.