The Determinant Mutual Information (DMI) mechanism of Kong (2020, 2024) is dominantly truthful within the class of *consistent* reporting strategies, those that apply the same single-task strategy to every task. In settings where agents see multiple tasks before reporting, such as peer grading or peer review, it is natural to consider *joint-task* strategies that may condition reports on the full signal vector. Perhaps surprisingly, we show that the DMI mechanism preserves truthful reporting as a best response among all joint-task strategies when other agents play consistent strategies, so that truthfulness remains a Bayes--Nash equilibrium in the joint-task class. Without the restriction of peers to consistent strategies, however, both dominant truthfulness and informed truthfulness fail against joint-task peer strategies.

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