I am going to make the following conjecture:
In an evaluation scale (e.g, rate this professor on a scale of 1 to 5), the mean evaluation is biased toward the middle.
Is this conjecture false? Is it true, but widely known? If it is true but not published, then someone should formally prove it and submit it to a journal.
Your errors are being drawn from a trucated distributions. In this case your distribution is trucated fom both ends and so variance is artificially low. Thus your covariance will be artificially low. If I rember correctly this is covered in Greene