A Tool to Complement Human Intelligence: the Math Behind Human Indispensibility

Much ink has been spilled recently on the existential risks and potential of Artificial Intelligence. Between breathy utopian think-pieces and apocalyptic proclamations of the end of meaning in human life, an entire spectrum of outlooks muddies the waters on insight-driven and human-focused paths forward. While philosophical musings and abstract plans are prevalent, relatively little attention has been paid to underwriting integrative deployment as a problem which yields to analysis. The question 'when should an autonomous system step in' is typically framed as demanding a comprehensive world-model of the human subject- oppositional defiance and counter-picking make this approach undesirable, turning the human and AI against one another. Instead, by combining operationalization from psychology, Pareto optimality from economics, norm-based stability from robust controls, and shortest-path algorithms from graph theory, we are able to present mathematically robust conditions under which heterogenous systems provide superior performance to unitary agents, guaranteeing a lower bound on efficacy of joint human/AI teams endorsed by relative advantage. We also derive implicit conditions under which such relationships hold, finding them to be of geometrically increasing scope as task complexity increases. Finally, we demonstrate these relations are not merely theoretical, using sample tasks with adversarial complexity to challenge the assignment paradigm, and find the results to remain within an order-of-magnitude of the predicted robustness condition.