Knowing Is Not Deciding: Symmetry Breaking and Ownership in Multi-Agent Systems

Teams of AI agents open competing fixes for the same failing test. Two support agents both answer the same customer, or neither does. These failures occur with sufficient information, so a stronger LLM does not remove them. Our companion paper, Global Coherence (arXiv:2610.02036), asked whether a team knows enough to act. This paper asks whether a team that knows enough can decide. That takes two things beyond knowledge: symmetry breaking and ownership. Agents that run the same program on the same view make the same choice, however capable the model. The obstruction theorem gives the exact condition under which such a team can act validly, and its price: singling out one of n agents takes log2(n) bits. Random draws tell agents apart but never reveal a hidden fact, and the harness, not the model, should draw them. Ownership keeps a choice made: forgetting the owner costs time exponential in the length of the work. The theory calls for one new harness component, a claim ledger that records who owns each contested choice. Seven pre-registered studies on LLM agents show both obligations at work. Stating the missing fact restores sufficiency: it solved 80 of 80 hidden-fact tasks, but only 4 of 80 symmetric ones, where the agents knew everything and still could not tell themselves apart. Symmetry breaking (a harness draw, or names on a shared roster) and ownership (an owner the harness records) each solved 79 to 80 of the 80 symmetric tasks and left hidden-fact tasks at chance. More reasoning effort fixed neither. This double dissociation replicates on models from a second provider. Ownership must also last: a four-session task took 17.3 sessions when its owner was forgotten, against 4 with a claim ledger.