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Sprint projectOct 26, 2026Kyoto, Japan (online)

Auditing Feasible Improvements at Recorded Coalition Rewards

Takahiro Tsuchiya

Submitted to AI Collusion Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.

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Which rewards remain protected, and how many final assignments may change? We study exact audits of additive unique-task allocations from the Colosseum Jira starter. Among 64 outcomes from eight tasks, joint improvements number 44 under coalition-aggregate protection, 43 under both groups and 29 under individual floors. One changed assignment finds all 29 individually protected positives; full search raises nine optima without adding classifications. Separate 48 outcomes from twelve tasks yield 38, 26 and 19, again with all individual positives found by one change. Serial one-agent paths attain the full individual-protected optimal value in every record while preserving original floors. The earlier delivery comparison retains its partial 33/48 view and exploratory technical continuation, with no amended randomization p. We also compare optional advice in 36 fresh four-agent allocation revisions of twelve known matrices, sharing full information and actor order. After explicit technical continuation, endpoint and path produce identical J on all twelve tasks. Their mean contrast with no advice is 2.9529 J, entirely from one case with eleven ties; path-minus-endpoint is zero. Both Holm-adjusted sign-test p-values are 1. Protected positives are 6/12 in all three arms; step-floor breaches are 1, 0 and 0. Neither robust benefit nor added path-presentation value is demonstrated. Exact witnesses and paths separate mathematical attainability from observed advice responses, without establishing intent, communication causality, detector accuracy, human benefit or deployment efficacy.

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  1. This project provides a useful way to ask whether an allocation can be improved while preserving specified rewards. Comparing coalition-level, group-level, and individual protections is a particular strength: it shows why protecting an aggregate does not necessarily protect every participant. The exact witness assignments and reported independent verification make the auditing approach concrete and checkable.

    The evaluation also includes valuable comparisons with simpler alternatives. Finding that a single-agent change identifies every individually protected improvement case helps clarify where full optimization adds value. The optional-advice experiment is reported honestly, including the lack of demonstrated additional benefit from presenting an explicit path.

    The main opportunity is to make the practical contribution easier to see. A shorter summary centered on one worked example, the key protection tradeoffs, and the distinction between attainable improvements and observed behavior would improve accessibility. Further testing on larger or less fully specified environments would help establish where the audit offers useful advantages over simpler methods. Overall, this is a careful and worthwhile contribution to multi-agent auditing.

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Cite this project

@misc{tsuchiya2026auditing,
  title = {{Auditing Feasible Improvements at Recorded Coalition Rewards}},
  author = {Takahiro Tsuchiya},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/auditing-feasible-improvements-at-recorded-coalition-rewards-eqyx}},
  url = {https://apartresearch.com/sprints/projects/auditing-feasible-improvements-at-recorded-coalition-rewards-eqyx}
}

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