  Recently a growing literature study a new forecast aggregation setting where
each forecaster is additionally asked ``what's your expectation for the average
of other forecasters' forecasts?''. However, most theoretic results in this
setting focus on the scenarios where the additional second-order information
helps optimally aggregate the forecasts. Here we adopt an adversarial approach
and follow the robust forecast aggregation framework proposed by Arielia,
Babichenkoa, and Smorodinsky 2018. We delicately analyze the
possibility/impossibility of the new setting when there are two forecasters
that either are refinement-ordered or receive conditionally independent and
identically distributed (c.i.i.d.) signals. We also extend the setting to a
higher level of expectation setting where we can additionally ask ``what's your
expectation for the other forecaster's expectation for ...''. The results show
that in the above settings, the additional second-order information can
significantly improve the aggregation accuracy, and the higher the order, the
higher the improvement.
