We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar distributional property $\Gamma$ if and only if $\Gamma$ is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property $\Gamma^1$ is not elicitable by itself, but is elicitable conditionally on another elicitable property $\Gamma^0$, then there is a canonical algorithm that jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.

翻译：我们在多校准与属性引出之间建立联系，并证明（在温和技术条件下）能够为连续标量分布属性$\Gamma$构造多校准预测器当且仅当$\Gamma$是可引出的。在否定方面，我们证明对于不可引出的连续属性，存在简单数据分布使得即使真实分布预测器也未得到校准。在肯定方面，对于可引出的$\Gamma$，我们给出了批处理和在线对抗设置下的简单规范算法，可学习$\Gamma$-多校准预测器。这推广了以往关于多校准均值与分位数的工作，并实际上强化了现有的在线分位数多校准结果。为进一步平衡我们的否定结论，我们证明：若属性$\Gamma^1$自身不可引出，但在另一个可引出属性$\Gamma^0$条件下可引出，则存在规范算法可联合多校准$\Gamma^1$和$\Gamma^0$；这推广了以往关于均值-矩多校准的工作。最后，作为我们理论的应用，我们为公平（多校准）风险评估提供了新颖的算法结果与不可能性结果。