Surface volumes of rounding polytopes

The paper determines the vertices and surface volumes of all rounding polytopes for commonly used rounding methods: the quota method of greatest remainders, and the divisor methods. These methods are used to round continuous non-negative weights summing to one to non-negative integers summing to a predetermined accuracy, e.g. to 100 when rounding to percentages. Our results are of interest when average properties of rounding methods are investigated, and an example from political science is included.