On rounding off quotas to the nearest integers in the problem of apportionment

Abstract

Simulations are performed in order to make comparisons among five methods of U.S. Congressional apportionment. Specifically, the probability is estimated under each method of apportionment that the number of Representatives allocated to a state is equal to the number obtained by rounding off the quota of that state to the nearest integer. According to the Webster method, numerical evidence shows that the probability is 97.6 percent on average.