I was looking at the marginal case because it is the easiest to see. Once you accept that this is the case (which, as I pointed out in another comment is an emp

I was looking at the marginal case because it is the easiest to see. Once you accept that this is the case (which, as I pointed out in another comment is an empirical question; it is not a-priori obvious that I am correct), the question becomes how big is the effect. If it is sufficiently large, then it would be sufficient to overcome significant differences in objective measurements. Again, this is an empirical question.