On Methods for Rounding Probabilities and Other Fractions

Abstract. This paper determines the vertices and surface volumes of all rounding polytopes for the most commonly used rounding methods: the quota method of great-est remainders and the divisor methods. These rounding methods are used to round continuous non-negative weights summing up to one to non-negative integers summing up to a predetermined accuracy, e.g. to the accuracy 100 for rounding to percentages. The rounding polytopes that we characterize are de¯ned as the set of weights rounded to a given ¯xed rounding result. Our results are of great interest if average properties of rounding methods are being investigated. To illustrate this we review an application of our results in political science. 1.