EM list: As before, I start with that unwritten standard factor as Pij, and then adjust the result afterwards for how the method's conditions differ from the ones that are assumed by that standard probability factor. So, without Pij, the utility expectation change for each pair vote diifference is (Vi-Vj)(Ui-Uj). There are 3 candidate pairs that you vote between, and so the above expression is used in 3 terms: 1(Ua-Ub) + 1(Ub-Uc) + 2(Ua-Uc) [You're voting a double vote-difference between A & C]. Collecting terms, that is: 3Ua-3Uc Since Ua is 1 & Uc is 0, that expression equals 3. But, when we adjust for the fact that a greater total number of vote-difference is voted in Borda, by each voter, because, on the average, each voter votes a vote difference of 4/3 per candidate pair, we have to multiply that 3 by 3/4, and we get 9/4 = 2.25 So 2.25 is Borda's table entry. Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
