Popularity ranking does not work with many subjects, because reality exists independently of popularity, and is not achieved by common consensus. As Google grows further away from its roots, it becomes more bizarre in ranking pages.
Galileo was not thinking the popular choice when he re-asserted that the earth rotated the sun. Pasteur was not promoting the popular choice when he told doctors to wash their hands. Popularity is a transient phenomenon. Betamax was popular at one point in time. Eight track tapes were popular at one point.
Galileo summarized the problem with this type of ranking long ago:
"I seem to discern the belief that in philosophizing one must support oneself on the opinion of some celebrated author, as if our minds ought to remain completely sterile and barren unless wedded to the reasoning of someone else."
I've seen many times that PageRank is a big factor in determining results order. Websites that just republish content outweigh original sites that have a lower PageRank. The problem with link popularity is that when you don't have it, almost nobody finds you or links to you and when some important website links to you, other sites start to link to you and then people find you even for queries that are not so relevant to your site.
Google just didn't solve the problem of finding good content per se, they just avoided it by letting the other sites to decide about that.
Related:
ExpertRank - find the best, not the biggest
What Google, Yahoo and MSN think about the future of search