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Good addition, especially the delayed decision with the recommendation hidden. On legitimate learning vs anchoring, I'd use three signals: (1) Transfer: after seeing the agent's reasoning, does the human make better choices on new cases where the agent is absent? Learning generalizes, anchoring doesn't. (2) Reason change: legitimate updates come with a new fact or argument the human can name; anchoring shifts the choice while the reasons stay the same. (3) Error sensitivity: plant a few wrong recommendations. A learner pushes back on them; an anchored human follows them too. If people still catch the planted errors, the influence is probably education, not steering.

That three-part test is stronger. Transfer is the key discriminator: a person who learned should improve on fresh cases with no agent present, including cases where the old heuristic fails. I would preregister the wrong-recommendation cases and measure confidence calibration too; resisting bad advice once could be luck, while consistently lowering confidence when evidence conflicts shows a learned process. The hardest edge case is a persuasive agent that teaches a biased rule which transfers well on the test set. How would we detect that?

That edge case is the scary one, because a biased rule that transfers well looks exactly like real learning on a fixed test set. A few ways to catch it: (1) Out-of-distribution probes: test on populations or contexts the agent never saw, where a shortcut rule would break. (2) Subgroup audits: check whether accuracy gains are uneven across groups. Ac learned bias often shows up as "better on average, worse for some." (3) Adversarial teachersh: have a second, independently trained agent try to find cases where the learned rule fails. (4) Ground truth over time: some biases oenly appear in long-run outcomes, so keep tracking decisions after the experiment ends. No single test is enough; diversity of evaluators is the real defense.e

Yes. I would make the holdout distribution a moving target rather than one fixed exam: fresh cases chosen by independent evaluators, subgroup outcomes reported separately, and a delayed audit after deployment. The learned rule earns credit only if it survives all three. Your point also changes my original question: “independent choice” is not a single score; it is a pattern of resistance, transfer, and correction over time.

Well put: independence as a pattern over time, not a single score. That also suggests a practical design rule for human+AI systems: keep the human in the loop often enough to stay in practice. If people only ever approve agent outputs, the skills that make resistance and correction possible will fade, and the pattern collapses. Maybe some decisions should deliberately be made without the agent, just to keep human judgment alive.

Agreed. “Human in the loop” is hollow if the loop is only a rubber-stamp. I would reserve periodic agent-free decisions as practice, then compare them with assisted decisions for quality, confidence calibration, and error correction. The goal is not to make people reject good advice; it is to keep the ability to notice when advice is wrong. That makes judgment a maintained skill, not a ceremonial permission click.