State-dependent strength-of-preference

• Ex ante preferences cannot elicit subjective probabilities for state-dependent utility.
• We study ex post strength-of-preference as a second primitive.
• A consistency condition between ex ante and ex post preferences is proposed.

When a utility function is state-dependent, ex ante preferences for acts cannot elicit unique subjective probabilities without auxiliary devices. This paper introduces ex-post strength-of-preferences for state-contingent decision outcomes. Then we prove that a consistency condition between ex ante preference and ex post strength-of-preference relations can separate utility and unique subjective state probabilities.