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If you analyze the results of a relatively uncompetitive phrase you could probably rank very well just by tweaking keyphrase weights. If you then take this knowledge and try these same weights on a competitive phrase, your results are not going to be nearly as good.
Beacause the first set of results was uncompetitive, the SEO/webmaster that designed those pages didn't need to match the algo as closely. With the second set, the pages were probably tweaked to perfection and had lots of good incoming links. So it's not really seperate algos, its just that some serps are closer to the actual algo than others.
There's all kinds of white papers about different forms of link popularity...
"a list of the elements"
I myself haven't done any research to seperate all the factors in a numerical order. Generally the title, text, and links are going to play the biggest role in your listing.