On the plurality functions (Q1323545)

Let \(P_ n\) be the set of \(n\)-tuples of nonnegative reals, not all 0. Solving problems posed by \textit{F. S. Roberts} [Aequationes Math. 44, 124 (1992)] in the context of the theory of choices, the author offers the general solutions \(f:P_ n \to P_ n\) of the conditional functional equation \(f(x + y) = f(x) f(y)\), supposed to hold for all \(x,y \in P_ n\) for which \(f(x) f(y) \neq 0\). In particular cases, symmetric and/or homogeneous solutions, those whose range is the set of \(n\)-tuples of 0's and 1's (not all 0's) and the question of extension are also examined. Another paper on the subject, by G. L. Forti and L. Paganoni, is forthcoming in Aequationes Math.