Concave additively decomposable representing functions and risk aversion

A condition for preference relations on Cartesian products is introduced, the concavity assumption. It gives the behavioural foundation to concave additively decomposable representing functions (prominent in optimization). Its connections with strong separability (=coordinate or preferential independence) combined with convexity are studied. The cardinal coordinate independence condition, by itself necessary and sufficient for subjective expected utility maximization, is combined with the concavity assumption into concave cardinal coordinate independence, a concise condition characterizing the customary expected utility maximization with risk aversion.