Stochastic additive differences

Properties of a binary choice probability function $p$ defined on multiattributed outcomes are studied to represent $p$ as a transformation of additive difference evaluations of chosen and unchosen outcomes into the unit interval. We use an algebraic assumption to obtain an additive difference representation, but allow for restricting strict increasingness of the transformation to the subset of the domain on which transformed values are strictly between 0 and 1. We also apply a topological assumption to axiomatize the cases of homogeneous product sets in the context of finite-state decision making under uncertainty.