A paradox for supertask decision makers

Abstract

Infinite decision sequences, or supertasks, reveal a fundamental tension in the requirements of rationality. In certain games and reward-based decision problems, an agent can respond rationally to any single choice in a sequence, yet it remains impossible to respond rationally to every choice collectively, even when the decisions are independent. One such paradox involves a game where both players possess winning strategies—one derived from the Axiom of Choice and the other from a simple reversal rule—rendering it impossible for both to implement their strategies concurrently. A second puzzle employs a Yablo-style rule to show that no sequence of actions can satisfy the conditions for a reward at every step. These cases imply that ideal rationality cannot be fully captured by dispositional properties, as an agent may be unable to maintain rational behavior throughout a supertask despite being capable of doing so at any specific point. Furthermore, these puzzles serve as counterexamples to the deontic Barcan formula and the principle that a conjunction of rational requirements is itself a rational requirement. By demonstrating that an agent can be required to act a certain way at each point without being required to do so at every point, these scenarios challenge standard accounts of normative consistency in infinite contexts. – AI-generated abstract.