Abstract
We propose a per-task leverage ratio for human-agent collaboration: human work displaced by an agent, divided by the human time required to specify the task, resolve mid-run interrupts, and review the result. The denominator decomposes into three channels through which a conserved per-task information requirement must flow, each with its own time-cost scalar. We show that information density itself is directional and bounded by separate ceilings on human-to-agent and agent-to-human flow, and that the asymptotic behavior of leverage decomposes into two scaling axes (capability and memory) with a non-zero floor on the planning term set by irreducible task novelty bounded by human throughput. We extend this per-task analysis to a windowed leverage measure that accommodates recurring tasks, spawned subtasks, and amortized system-design investment. The per-task ceiling does not bind the windowed measure, though both remain bounded: L_{\text{task}} by per-task novelty, L_{\text{window}} by the stock of accumulated planning investment that pays out within the window. The framework operationalizes aspects of earlier qualitative work on supervisory control (Sheridan, 1992), common ground (Clark & Brennan, 1991), and mixed-initiative interaction (Horvitz, 1999) within a single normative ratio, and produces a list of testable empirical questions that we leave as open problems.
