Expected Value under Normative Uncertainty

Abstract

Maximising expected value is the classic doctrine in choice theory under empirical uncertainty, and a prominent proposal in the emerging literature on normative uncertainty, i.e., uncertainty about the standard of evaluation. But how should Expectationalism be stated in general, when we can face both uncertainties simultaneously, as is common in life? Surprisingly, different possibilities arise, ranging from Ex-Ante to Ex-Post Expectationalism, with several hybrid versions. The difference lies in the perspective from which expectations are taken, or equivalently the amount of uncertainty packed into the prospect evaluated. Expectationalism thus faces the classic dilemma between ex-ante and ex-post approaches, familiar elsewhere in ethics and aggregation theory under uncertainty. We analyse the spectrum of expectational theories, showing that they reach diverging evaluations, use different modes of reasoning, take different attitudes to normative risk as well as empirical risk, but converge under an interesting (necessary and sufficient) condition.