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The dampening factor takes it's percent (supposedly 12-15%) right off the top at each link, so that PR5 is actually a PR4.25
That's incorrect. The damping factor is applied to the real PR, not the the ToolbarPR which is on a logarithmic scale. Therefore, the result in your example is not ToolbarPR 4.25 but much closer to 5.
Also, the damping factor was taken into account for all of my statements.
Basically the difference, when running interations, is whether the PR5 coming into the site REMAINS a FULL PR5 (does not lose it's PR) with each successive iteration.
Of course, the page is losing PR by adding external links. If you have run simulations using the original PR algorithm, you can easily find this.
The other 'ISP' model isn't well defined in a mathematical matter, because it is depending on the iteration scheme used (i.e. this isn't a valid model).
If a PR4 site swaps links with aanother PR4 site, wouldn't it just cancel out any benefit? Would either (or neither) get a pagerank increase?
So to sum it all up:
The PR benefit for the two sites (summing up all real PR of all pages of both sites) is neglectible, except for some devaluation of other external links. (Taken from doc_z's post).
You can see another one here:
[webmasterworld.com...]