Before revision:  in the special case when there are  O(m) voters and candidates , the running time becomes O(m^{2.69}), or O(m^{2.5}) if there is a nearly-linear time algorithm for multiplying dense square matrices.
After revision:  in the special case when there are m candidates and n= O(m) voters and candidates , the running time becomes O(m^{2.69}), or O(m^{2.5}) if there is a nearly-linear time algorithm for multiplying dense square matrices.