The central core argument of PageRank is flawed. Hopefully they are working diligently on using searchers' clicks on items in SERP's to confirm what their clients really find relevant.
The core argument of PageRank served its purpose well for a while, until the no-follow and Google forcing webmasters to artificially change their pages occured. Let me explain. Any search engine (until AI and text analysis progresses to the level of human brains - somewhere in 2040 or later) needs human input. Let me explain. I have this beautiful algorithm that can pick-up 200 pages with the words 'blue widgets' in the text. How do I rank them? Some methods like keywords etc can reduce the 200 pages to say 20, but all 20 offer identical statistics. Here the PageRank method was a way for webmasters to say, hey! we are voting like this or like this.
Another way to have users or webmasters vote is via social websites. Hey! 2000 people voted that this site is very good in this category. (Hence some social websites not allowing Google to index them). And yet another way as Barry said is clicks from users. However, the way suggested by Barry is higly unlikely to be an efficient way of finding relevant content as it will introduce a positive loop only within the first 10 SERPS, i.e., if Google shows websites 1... website10, users will be likely to only click amongst these 10 websites.
IMHO a better way would be:
(01) Better contents analysis and scoring that includes the one page model as well as the multipage model. If Barry's website has 100 pages that fall within the cluster 'Fidel Castro', the search engine should be able to automatically score it higher than the one page from Wikipedia with only a page on the subject. It is more likely that as a user, I will find what I am looking easier in Barry's website than in Wikipedia.
(02) Human assisted feedback in terms of counting links (PageRank is an unecessary wasteful calculation) simple link counts and other similar simple statistics, plus feedback from the social web and blogs.
(03) Another method for scoring is to score pages that users clicked on adsense lower for the query! Simple logic dictates that the user did not find what he was looking on the page and clicked away! (Hear!,hear!)
Yannis<edited to remove doubled text>
Edited by bwelford, 11 May 2008 - 02:36 PM.