On strategy-proof direct mechanism of active expertise over strictly convex compact set

We investigate the problem of strategy-proofness in the active expertise process where the decision making are based on the messages of experts who can distort the information for their benefit. In our model the expertise result is the arithmetic mean of expert messages and the opinion space is the multi-dimensional strictly convex compact set. We construct the corresponding direct expertise mechanism. We also prove that there is no strategy-proof direct expertise mechanism for this case. The problem of finding mechanism with minimum manipulation equivalent to the arithmetic mean expertise mechanism is formulated.