You write "Is it in fact the case that the difference between the 1st- and 2nd-best performer should shrink as the number of competitors goes up? This isn't obvious to me either way."
I think that, if you're drawing without replacement n times from a normal distribution, the difference between highest and second-highest value drawn should shrink as n rises, but that the opposite is true if the distribution is log-normal.
I would expect that "greatness" in terms of critical acclaim in some field is log-distributed, so, the bigger the field, the greater the extent to which the leader should stand out above the second-best.
You write "Is it in fact the case that the difference between the 1st- and 2nd-best performer should shrink as the number of competitors goes up? This isn't obvious to me either way."
I think that, if you're drawing without replacement n times from a normal distribution, the difference between highest and second-highest value drawn should shrink as n rises, but that the opposite is true if the distribution is log-normal.
I would expect that "greatness" in terms of critical acclaim in some field is log-distributed, so, the bigger the field, the greater the extent to which the leader should stand out above the second-best.