Collective Counterfactual Planning: Coordination, Consent, and Verification under Representational Constraints
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Abstract (arXiv)
Groups routinely complete projects that no single member can plan, execute, or verify alone. We propose a formal model of this phenomenon, Collective Counterfactual Planning (CCP), in which the binding limitation on each agent is neither capability, knowledge, nor observability, but representational geometry: each agent perceives the state, conceives moves, consents to actions, and certifies goal requirements only through a projection onto an agent-specific subspace of a common task space. Four gates jointly determine whether a team can reach a conjunctive goal and legitimately recognize that it has done so: the exogenous implementation coalitions required to perform each action, together with three representational gates -- conception, consent, and task-relative verification qualification. We define the Collective Counterfactual Solvability (CCS) problem, separating geometric feasibility, executable attainment, and validated completion. The results expose a positive-negative duality. Iterated cross-agent relay can unlock a solution that no one-shot pooling of individual plans contains, but any goal requirement depending essentially on the subspace dark to the entire team is unverifiable and therefore not validly completable, even when the trajectory accidentally attains it. Memoryless and audited consent further constrain different objects -- action directions versus cumulative trajectory states -- and neither dominates the other. A four-step exhaustive horizon-bounded solvability scheme is sound and complete under exact representation of the relay closure; restricted implementations remain sound on returned plans but need not be complete. The model gives one geometry for sequential mutual enabling, competent execution of steps whose purpose is invisible to the executor, forced sub-teaming at expertise boundaries, and completion that cannot be validly declared.
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References · 8
- 2021Convex optimizationcited by 2,515
- 2023The Linear Representation Hypothesis and the Geometry of Large Language Modelscited by 716
- 2013The Complexity of Decentralized Control of Markov Decision Processescited by 231
- 2020Open Problems in Cooperative AIcited by 168
- 2017Cooperative Epistemic Multi-Agent Planning for Implicit Coordinationcited by 8
- 2016Coordination Event Detection and Initiator Identification in Time Series Datacited by 3
- 2014A Formal Analysis of Required Cooperation in Multi-agent Planningcited by 2
- 2025Interpretation as Linear Transformation: A Cognitive-Geometric Model of Concepts and Meaningcited by 2
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