Binary interactions and subset choice

Subset evaluation and choice problems abound in practical decision settings. They are often analyzed with linear objective functions that value subsets as sums of utilities of items in the subsets. This simplifies assessment and computational tasks but runs a risk of substantial suboptimality because it disregards evaluative interdependencies among items. This paper examines a binary-interaction model that accounts for preference interdependencies between items. Ordinal and cardinal versions of the model are axiomatized and compared to the simpler linear model as well as the general model that incorporates all orders of interdependence. Comparisons of computational complexity for standard subset-choice problems are made between the linear and binary-interaction models.