I think this issue is all about identifying clusters in a list of points in a large vector space. In particular, you want a method to identify these clusters which is independent of linear transformations on the space. (Replacing one questions with n^2 questions corresponds to multiplying the weight of that question by n) I do not know much about this, but this seems like it is doomed to fail. In particular, it seems like if the points are in any kind of general position, then the whole thing looks like a large simplex, and there is no way to tell the difference between points. You will probably always be able to change the "clusters" by sdding whatever questions you want.

I think the way past this is to allow each individual to choose their own weighting on the questions signifying how "important" that issue is to them. I think there is an important difference between two people who agree on all issues but prioritize them differently, and it is not a problem that they can agree with a movement to different degrees.