Idempotent Equilibrium Analysis of Hybrid Workflow Allocation

This paper dives into how humans and AI might split tasks in future workflows, modeling it as a repeating delegation process that settles into a stable setup where each job goes to whoever has the edge. Using math from lattice theory, it proves there’s always at least one such balanced point and spells out when it’s the only one, while a continuous version shows the steady-state automation level as x* = α / (α + β), with α as automation speed and β as the flow of new human-focused tasks, meaning full robot takeover is off the table if β stays positive. It tests this across three dynamic scenarios like discrete updates, evolutionary dynamics, and a beta-distributed task range, all landing on the same hybrid outcome, plus simulations from 2025 to 2045 forecast automation jumping from 10% to 65%, still leaving humans about a third of the work in a fresh role as workflow orchestrators. Wrapping up, it touches on boosts for skills, better benchmarks, and AI rules to push human-AI partnerships for max benefits.