Utility functions that lead to the likelihood ratio as a relative model performance measure

In this paper, we adopt the point of view of a decision-maker who evaluates a probabilistic model based on the test-sample averaged utility of the expected-utility optimal strategy that the model suggests in a horse race setting. After briefly reviewing the basic properties of the resulting performance measure for probabilistic models, we show that such a measure ranks two models according to their likelihood ratio if and only if the performance measure is based on a generalized logarithmic utility function. Thus, we provide a new decision theoretic motivation of the likelihood ratio as a model performance measure.