Cearly the schools are concerned with their published numbers -- they want to not only have the best and brightest, but to have a standard metric for communicating that fact to the public (ie, the avg GMAT score). So what is a great way to try and boost up your average score? Tell applicants that you'll take their highest score no questions asked. If you're just going to average my score, what incentive do I have to retake -- after all, if I do worse on the retake, I'd have to perform better on yet another retake just to get my average score back to where I started, so why retake and take that risk? Further, if I want to retake and boost my score, I would have to do significantly better than my original score -- if I score 690 and want to retake to get a higher score, I'd have to score in the upper 700s just to get a low/mid-700 score. That just seems like a crazy exercise to me!
So overall I'd be stunned if a school would actually average them (or at least tell us they would, even if they secretly take it into considering during deliberations -- but most schools have you self-report your score which they then verify if you're admitted, so they may not even see anything other than what you tell them, that is your highest score).
The sheer futility of retaking if your scores are averaged is what made me curious whether any specific schools actually did average GMAT scores or some other policy of not taking the highest. So far nobody has been able to list any?