Bucklin is sometimes described as the method which gives the win to the candidate with the highest median rank, analogous to Borda as the method that gives the win to the candidate with the highest average rank.
The usual version of Bucklin uses only the crude median, and then (in the case of several candidates tied for the highest median rank) gives the win to the candidate with the greatest number of ballots ranking him/her at or above the (common highest) median rank, i.e. the highest value of M+A in the notation used below. Here's how to detect which of several candidates has the highest generalized median rank when they all have the same ordinary median rank: For each candidate calculate the quantity Q = (A-B)/(M+0^M) , where A is the number of ballots above the median rank, B is the number below median rank, and M is the number at the (common) median rank. [The term 0^M merely serves to keep Q defined even when M=0, in which case A=B, so Q=0.] The candidate with the highest value of Q has the highest generalized median rank (among the candidates having the same ordinary median rank). This doesn't mean that the value Q is the generalized median rank; it isn't. But it does detect the generalized median rank order. Notice that this order reverses when the ballot rankings are reversed, so the generalized median order satisfies a strong reverse symmetry criterion like Borda does. To get a better picture of the generalized median, make a histogram of the candidate's ballot ranks. Cut the histogram area in half with a vertical line. That line marks the generalized median rank for the candidate. Forest > > ---- > Election-methods mailing list - see http://electorama.com/em for list info > ---- Election-methods mailing list - see http://electorama.com/em for list info
