Decomposing a Utility Function Based on Discrete Distribution Independence

For two-attribute decision-making problems, the multilinear utility model cannot be applied when the risk aversion on one attribute depends on the level of the other attribute. We propose a family of general preference conditions called nth-degree discrete distribution independence that can accommodate a variety of dependence relationships between two attributes. The special case of second-degree discrete distribution independence is equivalent to the utility independence condition. We focus on third-degree discrete distribution independence that leads to a decomposition formula that contains many other preference models as special cases.