Ordinal One-Switch Utility Functions

We study the problem of finding ordinal utility functions to rank the outcomes of a decision when preference independence between the attributes is not present. We propose that the next level of complexity is to assume that preferences over one attribute can switch at most once as another attribute varies from low to high. We refer to this property as ordinal one-switch independence. We present both necessary and sufficient conditions for this ordinal property to hold and provide families of functions that satisfy this new property.