On preferences with infinitely many subjective states

Models with subjective state spaces have been extremely useful in capturing novel psychological phenomena that consist of both a preference for flexibility and for commitment. Interpreting the utility representations of preferences as capturing these phenomena requires one to use the notion of a sign of a state. For linear preferences, we completely characterise the sign of a state in terms of its analytic representation as an integral with respect to a signed measure. In models with finitely many states, a state is either positive or negative, but never both. We show that in models with infinitely many states, a state can be both positive and negative. Thus, models with finitely many states may not capture all the behavioural features of an infinite model. Our methods are also useful in constructing utility functionals over menus with desired local properties.