  We present a novel methodology for identifying public knowledge and
eliminating the biases it creates when aggregating information in small group
settings. A two stage mechanism consisting of an information market and a
coordination game is used to reveal and adjust for individuals' public
information. A nonlinear aggregation of their decisions then allows for the
calculation of the probability of the future outcome of an uncertain event,
which can then be compared to both the objective probability of its occurrence
and the performance of the market as a whole. Experiments show that this
nonlinear aggregation mechanism outperforms both the imperfect market and the
best of the participants. .
