Part of the confusion derives from identifying PR with what's on the toolbar. Further muddying this discussion is identifying what's on the toolbar with inbound links, as well as not making the distinction between the toolbar PageRank and the real PageRank at the Plex.
The way I understand it, Real PageRank is an indicator of how important a site is and helps determine the likelihood of how many clicks through a site a "random surfer" will go before becoming bored and leaving. This is one reason why directing links to inner pages and sections of pages helps because PageRank can be set to dampen on individual pages as well as groups of pages.
Even at the beginning, if you read the Anatomy of a Search Engine paper
[ilpubs.stanford.edu], the creators of PageRank were aware of the inherent limitations of PR itself for determining relevance and they were already experimenting with position of the links on a page as well as the words surrounding the link to help improve accuracy. In the beginning they were highly focused on the Authority/Quality of a page and they used PageRank as a measure of that.
However that measure was flawed because the authors may not have been sufficiently focused on User Intent, as evidenced in the Appendix of the Anatomy paper, where the authors cite their number one result for the phrase, Cellular Phone, which was a web page about the dangers of cell phone use while driving. The authors cited the importance
of that page as justification for it being the number one result. They were unaware of or willfully ignoring the commercial intent inherent in the search phrase, Cellular Phone.
...The goals of the advertising business model do not always correspond to providing quality search to users. For example, in our prototype search engine one of the top results for cellular phone is "The Effect of Cellular Phone Use Upon Driver Attention", a study which explains in great detail the distractions and risk associated with conversing on a cell phone while driving. This search result came up first because of its high importance as judged by the PageRank algorithm, an approximation of citation importance on
Do you see how Google's founders equated the PageRank algorithm with the importance of a web page? But the importance of a web page is just one part now, one door of many that have to be crossed in order to reach the top of the SERPs. As pointed out by another member, a low PageRank web page can outrank web pages of higher rank. I will add to that and say lower PageRank links, that are linked in a specific way to maximize relevance can and do push a site to the top of the SERPs. There is a whole lot more going on beyond the PageRank of a site, including additional signals of importance (which is how I see Panda).
Nevertheless this is an interesting window in what PageRank represented (an indicator of importance), and how it was not the only spice in the recipe (because they were already experimenting with additional signals).
[edited by: martinibuster at 7:31 pm (utc) on Nov 4, 2011]