I have a question regarding the estimation of partworths or generally utiles for an ACBC survey using HB. Going through the various technical papers provided on this topic (ACBC techpap 2014,CBC/HB Techpap v5, 2007 Sawtooth proceedings, Otter p.111ff) I am unable to find a formula for the underlying utility / preference model for an arbitrary stimulus within the choice sets. Using classic CBC, the utility model is additive (compensatory) . Since ACBC includes must-haves and unacceptables, I would expect to see a non-compensatory/ multiplicative utility model , i.e. a single partworth becomes zero by unacceptable rule, the whole stimulus' utility becomes zero. Following the below statements from the mentioned papers, I assume, all three sections are coded as simple choices similar to CBC (Otters scaling optimization between sections aside). Must-haves and unacceptables are regarded as "rejected concepts" where utility is below the "None" threshold and the chosen concepts' utility model is the sum of the relevant utility models (partworth/vector) per attribute, i.e. compensatory estimation.
"The information in the core three sections of the ACBC questionnaires can be coded as a sequence of choice tasks and may be estimated using maximum likelihood estimation under the MNL model" (ACBC techpap 2014)
"add up the part worths (elements of ßi ) for the attribute levels describing the kth alternative (more generally, multiply the part worths by a vector of descriptors of that alternative) to get the ith individual’s utility for the kth alternative" (CBC/HB techpap v5)
"The discussion so far has ignored the rejection of alternatives by rules. Consider an observed response to a rules question (see Section 2) causing multiple alternatives left in the pool to be jointly marked as rejected." (2007 Sawtooth proceedings, Otter p.111ff)
"In the case of ACBC, any information extracted from all three parts of the interview pooled across respondents implies the transfer of information from one person’s SCREENER data to another person’s CBC data. This is because what is unacceptable or a must-have is very likely to differ across respondents. Thus, a model that suitably connects all three parts of the interview is essential for pooling across respondents to make sense." (2007 Sawtooth proceedings, Otter p.111ff)