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Merit estimations from paired comparison tests

I am trying to estimate merits from the data collected during a paired
compairison test.  One suggested method involves minimizing the error of
Log[ p(i)] estimates using a Least Squared approach and another suggested
method invloves using a Maximum Likelihood approach to estimate p(i) and
then taking the Log[p(i)].  The scaling is somewhat diffrerent between these
two approaches.  Can anyone advice me on why, which is more reasonable, etc.
Or does anyone have any other advice?

Many Thanks