Patri Friedman (of the Google group that experiments with internal prediction markets) scratched the issue but did not offer much elaboration, alas.
Maybe Bo Cowgill, who is one of our Post Authors, will lighten us (here, or on his blog), one day, on how that dual concept is implemented at Google.
Did I touch on this issue here? http://www.midasoracle.org/2006/10/12/prediction-markets-junk-science/
How about “Predictiveness for a given class of event is inversely proportional to the variance of outcomes against probabilities (as estimated by prediction markets)”?