Hi Bryan,
the above transformation differs from what is recommended in the MaxDiff Technical Paper. The main difference from my perspective is, that in the Technical Paper it is recommended to use the zero centered diffs transformed raw utilities, whereas you talk about the raw utilities.
From what I know, I would say, that it makes more sense to take the raw utils because only these utilities will deliver the correct probabilities. But then the nice explanation in the Tech Paper that the expected utility of the competing items is 0 and that for this reason you have to add a-1 in den denominator does no longer make sense, since the expected utility for the other items is different from zero ( when you do not apply the zc diffs transformation).
Do you have any advice whether I should use the raw utility or the zero centered diffs transformed utility?
Many Thanks
Rainer