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Converting MaxDiff utilities to 100-centered

Hi - I know there are a lot of similar topics on this forum. I have searched for hours across all the different questions and can't quite seem to find the answer to my question (though that might jus be misunderstanding some of previous posts).

I have inherited a MaxDiff analysis and I'm trying to figure out how they are calculating the anchored scores. I have a dataset with individual utilities and average utilities for a segment. I also have anchored scores at that segment level, but not at the individual level. By anchored scores, I mean the average utilities for a segment were converted to a set of 100-centered numbers. Ultimately, I want to calculate anchored scores for different cuts in the data, thus I want to be able to convert the scores at an individual respondent level so I can aggregate in many different ways.

In my research, I found this equation eUi / (eUi + a - 1) - which I can use to convert the utilities so the figures add up to 100. But, how can I get 100-centered figures instead?

Here is what I'm seeing. My ask is if you can help me figure out how to get closed to the Anchored score column using the utilities, then I'll be able to re-create at the individual respondent level.

Attribute   Utility   Anchored score
A                     .67                151
B                    -.52                64
C                    -.14                87
D                    -.00069         97
E                    .22                  114
F                    .35                   124
G                    -.58                 61
asked Sep 5, 2017 by cyi106 (120 points)

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