Suppose we have a finite sum of nonnegative numbers that equals 1: (*) x_1 + ... + x_n = 1 . Because TV viewers are so easily confused by several digits beyond the decimal point, we want to convert (*) to a sum of integer percentages P_j in the most felicitous, or the least infelicitous, way: P_1 + ... + P_n = 100% For example let n = 3. Then we want to map the points on the triangle {(x,y,z) in (R_0)^3 | x + y + z = 1} to the discrete set of 5151 points {(M,N,P) in (Z_0)^3 | M + N + P = 100} (where R_0 and Z_0 denote the nonnegative reals and integers, respectively). One obvious thing to try is to minimize the sum of squared error: So let (**) E(M,N,P) = (x-M)^2 + (y-N)^2 + (z-P)^2 and pick (M,N,P) such that E(M,N,P) is minimized. For the sake of this question, let's ignore the measure 0 of cases where the (M,N,P) minimizing (**) is not unique. Questions: ---------- 1. Let n > 0 be arbitrary. Is there a good algorithm for applying (**) in practice, to get the quantization (x_1,...,x_n) |—> (P_1,...,P_n) ??? 2. Is there a better or more useful measure of error than sum of squared differences? If so, why is it better? —Dan