The paper by David Schmeidler introduces a new axiom of comonotonic independence, which weakens the von Neumann-Morgenstern independence axiom. This axiom allows for the representation of subjective probability and expected utility without requiring additivity. The paper discusses the limitations of traditional Bayesian statistics, where prior probabilities may not reflect the actual information used to assign them. Schmeidler argues that nonadditive probabilities can better capture uncertainty and provide a more accurate representation of decision-making under uncertainty. The paper presents a model where acts are defined as mappings from states of nature to outcomes. It introduces the concept of comonotonic independence, which states that if two acts are comonotonic, then certain combinations of them should be preferred based on their outcomes. The paper also discusses the implications of nonadditive probabilities, noting that they can represent uncertainty in a way that additive probabilities cannot. Schmeidler's model is based on the idea that preferences over acts can be represented by a nonadditive probability measure and a von Neumann-Morgenstern utility function. The paper shows that this model can be used to represent preferences that are not compatible with additive probabilities, such as those demonstrated in the Ellsberg paradox. The paper also discusses the implications of nonadditive probabilities for decision-making under uncertainty, noting that they can capture uncertainty aversion and other complex behaviors. The paper concludes that the new model provides a more general framework for representing subjective probability and expected utility, allowing for a broader range of decision-making scenarios to be analyzed. It also highlights the importance of nonadditive probabilities in capturing the complexities of real-world decision-making under uncertainty.The paper by David Schmeidler introduces a new axiom of comonotonic independence, which weakens the von Neumann-Morgenstern independence axiom. This axiom allows for the representation of subjective probability and expected utility without requiring additivity. The paper discusses the limitations of traditional Bayesian statistics, where prior probabilities may not reflect the actual information used to assign them. Schmeidler argues that nonadditive probabilities can better capture uncertainty and provide a more accurate representation of decision-making under uncertainty. The paper presents a model where acts are defined as mappings from states of nature to outcomes. It introduces the concept of comonotonic independence, which states that if two acts are comonotonic, then certain combinations of them should be preferred based on their outcomes. The paper also discusses the implications of nonadditive probabilities, noting that they can represent uncertainty in a way that additive probabilities cannot. Schmeidler's model is based on the idea that preferences over acts can be represented by a nonadditive probability measure and a von Neumann-Morgenstern utility function. The paper shows that this model can be used to represent preferences that are not compatible with additive probabilities, such as those demonstrated in the Ellsberg paradox. The paper also discusses the implications of nonadditive probabilities for decision-making under uncertainty, noting that they can capture uncertainty aversion and other complex behaviors. The paper concludes that the new model provides a more general framework for representing subjective probability and expected utility, allowing for a broader range of decision-making scenarios to be analyzed. It also highlights the importance of nonadditive probabilities in capturing the complexities of real-world decision-making under uncertainty.