Continuity and Completeness

Expected utility theory has three main axioms: completeness, continuity, and independence. Completeness is dubious in many normative settings, so what happens when completeness is dropped? This post, based on joint work with Kalle Mikkola, explains that there is a surprising difficulty.

Moral philosophers often reject completeness because they think that some goods are not fully comparable. But they still carry on making continuity arguments. They should be cautious about this.