Ranking - Domain Authority

DOMAIN AUTHORITY
Now that we have relevant pages the best way to perform a final ranking is to identify domain authority and the popularity of the individual page within each of those domains.

PageRank and TrustRank come into play here. How popular is the page with other sites. How many inbound links, relevance of the links, and where are the links coming from are key factors in ranking.

Domain authority is weighed more heavily for highly competitive keyphrases but to a slightly lesser extent for long tail and specialized searches like exact phrase seaches using quotation marks.

In our simplistic example, the #1 and #2 rankings changed due to PageRank and TrustRank factors simulating that these far outweigh synonyms, keyword density and other on-page factors.

Cited Resource
Google Librarian Central
How does Google collect and rank results
Anatomy of a Search