Additive representation for equally spaced structures
The author shows that in the equally spaced discrete case of additive conjoint measurement a simple necessary and sufficient condition can be given. The approach is similar to that of \textit{D. H. Krantz, R. D. Luce, P. Suppes} and \textit{A. Tversky} [Foundations of measurement (1971; Zbl 0232.02040)] and uses assumptions of restricted solvability, coordinate independence, an Archimedean axiom, a discreteness condition called the equally spaced condition, and the weak separability condition that for all i, x, y, \(v_ i\), \(w_ i:\) \[ x_{-i}v_ i\succcurlyeq x_{- i}w_ i\quad if\text{ and } only\quad if\quad y_{-i}v_ i\succcurlyeq y_{-i}w_ i. \] The range of each additive value function is then an interval of integers.
discrete case of additive conjoint measurement
scientific article; zbMATH DE number 4209945