For practical purposes any method based on rankings or range style ballots, can be closely approximated by a summable version. Since approval cutoffs can be incorporated into rankings and ratings, methods that require approval cutoffs can also be efficiently accomodated.
It's based on the idea that if you agree with me that A is best, B second best, and C third best, then it is likely that your ratings of the remaining candidates will be highly positively correlated to mine. If there are N candidates we need an array with M=N*(N-1)*(N-2) rows and N+1 columns. Each row number stands for one of the permutations of N candidates taken three at a time. If your ballot agrees in the order of the top three candidates with the ith permutation, then your rating or ranking (as the case may be) of the jth candidate is added into the ith row and jth column of the array. And a one is added into column (N+1) of that row. Each row of the summed array is a summary of the votes of one of the basic M factions, together with the number of voters in that faction. The first three numbers in the row are the ones in which the members of that faction are in precise agreement. The remaining numbers (divided by the faction size) represent average rankings or ratings of the other candidates by members of the faction. Since the dimension of the Array is N*(N-1)*(N-2) by (N+1) it grows as the fourth power of N. For 100 candidates the array would have only one hundred million entries, which is tiny by today's standards of data sets. It is practically infinitesimal compared to the 100 factorial possible permutations of the candidates. Forest ---- election-methods mailing list - see http://electorama.com/em for list info
