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We make a connection between multicalibration and property elicitation andshow that (under mild technical conditions) it is possible to produce amulticalibrated 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 propertiesthere exist simple data distributions on which even the true distributionalpredictor is not calibrated. On the positive side, for elicitable $\Gamma$, wegive simple canonical algorithms for the batch and the online adversarialsetting, that learn a $\Gamma$-multicalibrated predictor. This generalizes pastwork on multicalibrated means and quantiles, and in fact strengthens existingonline 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 onanother elicitable property $\Gamma^0$, then there is a canonical algorithmthat jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes pastwork on mean-moment multicalibration.  Finally, as applications of our theory, we provide novel algorithmic andimpossibility results for fair (multicalibrated) risk assessment.

The Scope of Multicalibration: Characterizing Multicalibration via Property Elicitation