Additive reprensentations of preferences, a new foundation of decision analysis: the algebraic approach

In Wakker (1989, "Additive Representations of Preferences, A New Foundation of Decision Analysis"), a new foundation of decision analysis was given. The main tool was a way to derive comparisons of "tradeoffs" from ordinal preferences, with comparisons of tradeoffs revealing orderings of utility differences. These comparisons of tradeoffs underly the construction of standard sequences in conjoint measurement theory. The restrictive structural assumption (every approach has its restrictive structural assumption) was of a topological nature, requiring continuity. This paper adapts the main results of Wakker (1989) to the algebraic approach, where a solvability condition is required which is less restrictive than continuity.