Subjective Error and Non-expected Utility

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As a result of this research program, I completed a paper entitled "Subjective error measure." I will explain its motivation and results. The decision-maker who complies with Savage's axioms can be regarded as evaluating each act by solving a statistical inference problem, in which the estimation error is measured by the squared-error loss function. However, it is more desirable to derive a loss function, as well as the utility index and the subjective probability, from the decision-maker's own preference. I weaken Savage's axioms to characterize the preference which is based on the loss-minimization in the sense that the decision-maker evaluates each act by solving a statistical inference problem, in which the estimation error is measured by some loss function which may be different from the squared-error loss function. Also, the paper provides two examples of preferences which are based on the loss-minimization with the loss function more general than the squared-error loss function.