Every subjective state space with Euclidean structure contains almost-objective events which arbitrarily closely approximate the properties of objectively uncertain events for all individuals with event-smooth betting preferences - whether or not they are expected utility, state-independent, or probabilistically sophisticated. These properties include unanimously agreed-upon revealed likelihoods, statistical independence from other subjective events, probabilistic sophistication over almost-objective bets, and linearity of state-independent and state-dependent expected utility in almost-objective likelihoods and mixtures. Most physical randomization devices are based on events of this form. Even in the presence of state-dependence, ambiguity, and ambiguity aversion, an individual’s betting preferences over almost-objective events are based solely on their attitudes toward objective risk, and can fully predict (or be predicted from) their behavior in an idealized casino. Copyright Springer-Verlag Berlin/Heidelberg 2004
