The problem is how to compare the quality of different hypothesis tests in a Bayesian framework without introducing a loss function. Three different linear orders on the set of all possible hypothesis tests are studied. The most natural order estimates the Fisher information between indicators of event and decision.
Gercsik, Vladimir and Kelbert, Mark
"On Comparison of Hypothesis Tests in the Bayesian Framework without Loss Function,"
Journal of Modern Applied Statistical Methods:
2, Article 12.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss2/12