Strength of Preference and Risky Choice

This paper provides conditions under which a utility function under risk can be legitimately interpreted to measure strength of preference between consequences. These conditions require that if a decision maker regards the preference difference between acts a and b to be the same as the preference difference between acts a′ and b′ for every state of the world, then the preference difference between a and b should be regarded as equivalent to the preference difference between a′ and b′. A key assumption is that a decision maker's preference differences between acts given one state of the world should be independent of common consequences given other states of the world. Usefulness of this result is discussed.