'Ambiguity aversion’ is typically defined to be a general preference for ‘objective’ over ‘subjective’ uncertainly, and accordingly typically modeled in a general Anscombe-Aumann (‘horse race/roulette wheel’) setting.
This talk argues for dropping the notion of two qualitatively different types of uncertainty, arguing that the natural setting in which to characterize the property of ambiguity aversion is one where the linear structure of exogenous objective probabilities is replaced with a linear (i.e., real-valued) purely subjective state space. Virtually all real-world economically relevant uncertainty (stock prices or interest rates, earthquake magnitudes or damages, rainfall levels) takes the form of such purely subjective real-valued variables.
In such a domain, some purely subjective events and bets can nevertheless be said to be ‘more objective’ than others, and event-smooth preferences over such ‘almost-objective’ bets will, in the limit, exhibit all the classic properties over preferences and beliefs under purely objective uncertainty. This allows for a definition of ‘induced’ attitudes toward objective and mixed objective/subjective bets derived solely from preferences over purely subjective bets.
Adopting and adapting previous work of the author and others, we propose a characterization of ‘ambiguity aversion’ defined in this setting of purely subjective uncertainty which links aspects of preferences over purely subjective bets, induced preferences over objective and mixed bets, and event-derivatives of preference functions over purely subjective bets.