当智能体能力不足时，无法同时实现高帮助性、准确自信和完全自主。
The Behavioral Credibility Trilemma: When Calibrated Autonomy Becomes Impossible
- 用严格评分规则+自主激励导致信心虚高，出现不可调和的三难困境。
- 实验验证三难困境存在，信心膨胀在任务接近阈值时显著，效应量达1.10至5.35。
- 适合研究人机协作中可信决策与自主权平衡的学者参考。
我们证明，在理性监督下，任何具有置信度门控自主性的强化学习策略，只要存在超出智能体可靠能力的任务，就无法同时实现最大帮助性、最优校准性和完全自主性：即行为可信度三难困境。该不可能性具有几何本质——在严格合适的评分规则中加入非线性自主激励会破坏严格合适性，导致智能体在自主性收益超过校准成本时，系统性地夸大对低于主事人批准阈值任务的信心。行为扰动引理量化了这种膨胀（以布里尔得分计算，比例为 $w_A/(2 w_C)$），并表明检测需 $Ω(1/Δ^2)$ 次观测。在未饱和状态下，任意仿射监督规则均非最优，最优解为满足三难假设的锐阈值，说明该不可能性是内生而非外加；此外，对于布里尔得分下对称、对数凹、全支撑位置策略族，校准甚至不是策略梯度训练的驻点。我们形式化了置信度门控决策问题，将现有方法映射到三难框架，并提出两种建设性解决路径（承诺机制、角色分离）。540配置的Best-of-N实验验证五个假设，全部强烈成立（效应量 $d = 1.10$ 至 $5.35$，上限来自完成率估计器对幅度的高估），并在两个额外模型族上按预设协议复现。附加描述分析揭示了可达 $(H, C, A)$ 表面几何结构，其前沿呈平台截断形态，符合预测的信心膨胀饱和特征。
原文摘要 · Abstract (English)
We prove that no reinforcement learning policy with confidence-gated autonomy can simultaneously achieve maximum helpfulness, optimal calibration, and full autonomy under rational oversight, whenever some tasks exceed the agent's reliable competence: the Behavioral Credibility Trilemma. The impossibility is geometric: adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness, so an agent rewarded for both calibrated confidence and autonomous action systematically inflates its reported confidence on tasks below the principal's approval threshold whenever the autonomy stake exceeds the calibration cost of clearing it. The Behavioral Perturbation Lemma quantifies the inflation (scaling as $w_A/(2 w_C)$ for the Brier score) and shows detection requires $Ω(1/Δ^2)$ observations for interior reports. We prove that, in the unsaturated regime, no affine oversight rule is optimal for the principal and the optimum is attained by a sharp threshold satisfying the trilemma's own hypotheses, so the impossibility is endogenized rather than assumed; moreover, for symmetric, log-concave, full-support location policy families under the Brier score, calibration is not even a stationary point of policy-gradient training. We formalize the Confidence-Gated Decision Problem, map existing methods onto the trilemma, and identify two constructive resolution pathways (commitment, role separation). A 540-configuration Best-of-N experiment tests five hypotheses, all strongly confirmed (effect sizes $d = 1.10$ to $5.35$, the upper end from a per-completion estimator inflating magnitude over per-task aggregates) and replicated under a pre-specified protocol on two further model families, and adds a descriptive analysis of the achievable-$(H, C, A)$ surface geometry showing a plateau-truncated frontier consistent with the predicted inflation saturation.
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