The crucial tactical problem confronting each faction in a cumulative voting contest is how to cumulate their votes so as to elect the maximum number of directors possible. It was in order to provide "a simplified and workable system of solving" this problem that Arthur T. Cole in 1950 published his article on the "Legal and Mathematical Aspects of Cumulative Voting." The equations presented by Cole have since become the accepted formulae for solving the mathematical problems of cumulative voting. In this article, the author demonstrates, however, that Cole's equations contain significant errors and may yield faulty results in some situations. He then sets forth a more rigorous and accurate approach to the mathematical problems involved in cumulative voting for the election of corporate directors.
Lewis R. Mills,
The Mathematics of Cumulative Voting,
1968 Duke Law Journal
Available at: http://scholarship.law.duke.edu/dlj/vol17/iss1/2