The Potential of Cumulative Voting To Yield Fair Representation

We prove that cumulative voting usually enables a minority population to achieve political representation corresponding to apportionment by Webster's method, which minimizes the absolute difference of per capita representation between the minority and the remaining majority population. The minority, of arbitrary size, can generally attain its `Webster-fair' share of n seats with probability greater than 75 per cent and otherwise, with probability at most 4 n/n+1 1 the minority can attain just one seat less than its Webster-fair representation. Furthermore, for two subpopulations, the potential representation yielded by cumulative voting is identical to that obtained from apportionment by Jefferson's method, and for more than two subpopulations the potential representation by cumulative voting cannot be greater than that of Jefferson apportionment. These results confirm the potential of cumulative voting to yield representation proportional or nearly proportional to population, and the results counter claims or concerns that cumulative voting would be unfairly advantageous to minority populations.