Convert max diff probability scores to % of respondents who prefer item

Question

Using Lighthouse Studio I have estimated respondent-level HB max diff  
scores (for a 10 item max diff) and reported results to my client using the
average/mean Probability scale score for each item. So, for example, results are similar to below where values represent average score for each item in the Total sample (and scores sum to 100 across all 10 items).

Item 1 score=20
Item 2 score=15
Item 3 score=7
Item 4 score=9
Item 5 score=1
Item 6 score=10
Item 7 score=5
Item 8 score=12
Item 9 score=8
Item 10 score=13

The client is interested in knowing how the reported probability scores translate to percent of respondent who want/prefer each item. So, for example, Item 2 has a score of 15 and the client wants to know what percent of respondents want/prefer Item 2 based on that average probability score of 15.

Are there any rules of thumb or best practices for converting average probability scale scores to percent of respondents who want/prefer each max diff item?

Thank you.

Answer 1

If you are using probability scores, then it is very simple per the proportional draw assumption of the logit equation (which we've assumed and used to estimate scores and get you to the point you are) to allocate the share of choice across respondents for a subset of the items.

The first step is to assume a consideration set of 2 or more items.  So, let's assume a consideration set of 3 items: items A, B, and C for illustration.  Let's also assume the probability-scaled scores are 10, 15, and 25 for A, B, and C, respectively for respondent #1.

For respondent #1, the likelihood of choice would simply be proportional to the scores, made to sum to 100, or:  20%, 30%, and 50%.  

Repeat this for all respondents and average the percentages across respondents.