One-Switch Conditions for Multiattribute Utility Functions

We introduce a variety of new independence conditions for multiattribute utility functions that permit preference dependencies among the attributes of a decision problem. The hierarchy of new conditions varies in the degree to which it specifies the functional form, ranging from more general solutions with weaker constraints, to more specific solutions with stronger constraints. This formulation provides a wealth of new functional forms that a decision maker may use in a multiattribute decision problem. In addition, it may be used to tailor the utility elicitation process to the comfort level of the decision maker. The new conditions, and the corresponding functional forms, are based on the idea of limiting the number of switches that a decision maker may make between two decision alternatives as a parameter of the problem varies. We show how this formulation also relates many widely used concepts in single and multiattribute utility theory.