I just recall that the projection postulate of QM in its straightforward form is not applicable to the observables with continuous spectra, e.g., to the position operator. Of course, continuous spectrum is an idealization for a real experiment. So, if the number of eigenvalues is "sufficiently" large then one can expect that the Luders projection postulate would not applicable. My impression that in this experiment the selection of fine scale played the crucial role. Question to the authors:
Would you agree that your effect was approached merely due to selection of the scale?
I suspect that for the dichotomous scale you would confront the problem posed in the paper: Khrennikov A., Basieva I., Dzhafarov E. N, and Busemeyer J. R. Quantum models for psychological measurements: an unsolved problem. PloS one, 9(10):e110909, 2014. pmid:25343581

From the psychological measurement viewpoint, I am curious whether people answering the questions in the 9-scale still treat it as discrete. Do they really distinguish sharply 1 and 2? May be for them this a good approximation of the continuous scale?
So, may be this