# [EM] A Clone Free Metric On Ballots Classic List Threaded 1 message Reply | Threaded
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## [EM] A Clone Free Metric On Ballots

 It was late last night when I wrote the first post so it was short on explanation ... so here is a brief explanation ...Every time one ballot ranks x before y and the other one doesn't, there is a discrepancy that separates them in ballot space. A complete reversal to y ahead of x is twice as serious as a mere change to equality in rank. To assure freedom from clone bias the discrepancy is weighted by the product P(x)P(y) where P is a probability.distribution that distributes P(x) among x1,x2,x3, etc. when x is is replaced by a set of closely clustered clones.The matrix manipulation keeps track of the count of weighted discrepancies... in particular, the entry in row x, column y of M1 is (supposed to be) a one if x is ranked ahead or equal to y, otherwise zero.So M1(x, y) minus M1(y, x) is one, zero, or negative one, depending on whether x>y, x=y, or x