I worked years ago on a research project that used a survey design that had two Likert scales for each statement. One measured agreement, the other importance. I've been asked about this again, and I can't recall what this is called. I'm hoping there is a survey expert out there that can remind me what this approach is called, and maybe point me to some examples I can share?
There are a couple of different approaches to this, but most of these approaches have very similar objectives. The idea is to weight satisfaction by importance. Say you asked respondents about how satisfied they were with seven different services, and then you asked them how important each of these seven different services were. If an individual is extremely dissatisfied with a service he/she thinks is very important, this is will likely contribute to greater dissatisfaction with the 'overall programme of services', than for example, if a person was extremely dissatisfied with a service they did not regard as important at all.
Let's assume your Likert data is on a five-point scale. You keep the satisfaction data as it is (1,2,3,4,5), but then you recode importance to range like (-2,-1,1,2,3). You then multiply satisfaction by importance for each item, and then average across all items. (Note how we did not include a 0 in recoding importance, because we do not want to multiply by 0.) You then may want to convert these into some sort of standard measures, ranging from 0 to 1, or some such.
The Cummins Comprehensive Quality of Life Scale is a good example of this. In the document I linked to, the author does a very good job of explaining how his scale should be calculated, and how results should be interpreted. In short, he asks about satisfaction with and the importance of seven different quality of life domains. The approach given by Cummins is more involved than the very brief sketch I gave above, but his full approach (too long to be summarized here) is definitely superior.