http://www.overcomingbias.com/2009/02/share-likelihood-ratios-not-posterior-beliefs.html

By Anna Salamon and Steve Rayhawk

Indubitably intriguing snippet:

When I think of Aumann's agreement theorem, my first reflex is to average. You think A is 80% likely; my initial impression is that it's 60% likely.  After you and I talk, maybe we both should think 70%.  "Average your starting beliefs", or perhaps "do a weighted average, weighted by expertise" is a common heuristic.

But sometimes, not only is the best combination not the average, it's more extreme than either original belief.