If you pay untrusted workers to train a model, you can audit a random step, score the final model on held-out data, or pay for agreement between redundant workers. We priced these as a hidden-action contract (a linear programme) in the programme verifiable-training-mechanisms.
Agreement. Over 4,000 random two-worker instances, an agreement term never made the cheapest honest-honest contract dearer and made it up to 97% cheaper. But once we also required that "both cheat the same way" is not an equilibrium, agreement was worth nothing in all 1,349 instances where cheaters share one trajectory. It still helped when cheaters cannot coordinate. The parameters were swept, not measured on real runs.
A lower bound. Any contract paying at least -S needs expected pay of at least max(C, g/p - S) against a cheat that saves g and is caught with one-sided resolution p. It held in 2,755 random instances and is exact for a binary audit. It is not within a constant factor in general (worst ratio 2,093) and says nothing useful for a Gaussian held-out score.
Two corrections along the way: a first sweep showed a spurious 80% saving that came from cheats agreeing with honest peers more than honest workers do, and a strictness margin that looked like a 0.2% saving. Both are in the research log.