  Peer prediction is a method to promote contributions of information by users
in settings in which there is no way to verify the quality of responses. In
multi-task peer prediction, the reports from users across multiple tasks are
used to score contributions. This paper extends the correlated agreement (CA)
multi-task peer prediction mechanism to allow the reports from users to be on
heterogeneous tasks, each associated with different distributions on responses.
The motivation comes from wanting to elicit user-generated content about places
in a city, where tasks vary because places, and questions about places, vary.
We prove that the generalized CA mechanism is informed truthful under weak
conditions, meaning that it is strictly beneficial for a user to invest effort
and acquire information, and that truthful reporting is the best strategy when
investing effort, as well as an equilibrium. We demonstrate that the mechanism
has good incentive properties when tested in simulation on distributions
derived from user reports on Google Local Guides.
