  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.
