This paper by David Schmeidler explores the concept of subjective probability and expected utility without the assumption of additivity. The author introduces the notion of comonotonic independence, which is a weaker form of independence compared to the von Neumann-Morgenstern (N-M) axiom. This new axiom allows for the representation of preferences over acts using a non-additive probability measure and a von Neumann-Morgenstern utility function. The paper demonstrates that if a nondegenerate, continuous, and monotonic weak order over acts satisfies comonotonic independence, then it induces a unique non-additive probability measure and a von Neumann-Morgenstern utility function. The expected utility with respect to this non-additive probability measure represents the weak order over acts. The paper also discusses the implications of non-additive probabilities in decision-making under uncertainty, particularly in cases where additive expected utility is not applicable. The main result is a theorem that extends the Aumann-Anscombe theorem to non-additive probability measures, showing that under certain conditions, a preference relation can be represented by expected utility with respect to a non-additive probability measure. The paper concludes with a discussion on the concept of uncertainty aversion and its mathematical characterization.This paper by David Schmeidler explores the concept of subjective probability and expected utility without the assumption of additivity. The author introduces the notion of comonotonic independence, which is a weaker form of independence compared to the von Neumann-Morgenstern (N-M) axiom. This new axiom allows for the representation of preferences over acts using a non-additive probability measure and a von Neumann-Morgenstern utility function. The paper demonstrates that if a nondegenerate, continuous, and monotonic weak order over acts satisfies comonotonic independence, then it induces a unique non-additive probability measure and a von Neumann-Morgenstern utility function. The expected utility with respect to this non-additive probability measure represents the weak order over acts. The paper also discusses the implications of non-additive probabilities in decision-making under uncertainty, particularly in cases where additive expected utility is not applicable. The main result is a theorem that extends the Aumann-Anscombe theorem to non-additive probability measures, showing that under certain conditions, a preference relation can be represented by expected utility with respect to a non-additive probability measure. The paper concludes with a discussion on the concept of uncertainty aversion and its mathematical characterization.