Greatest remainder bi-proportional rounding and the Greek parliamentary elections of 2007

Matrix scaling is the problem of assigning values to the elements of a matrix that are proportional to a given input matrix. The assignment should fulfill a set of row- and column-sum requirements. We propose a new method that differs from divisor-type methods appeared until now in the literature. This method combines the largest remainder apportionment and bi-proportional rounding. Exhaustive application to the Greek parliamentary elections of 2007 justify our effort.