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.