Read the original PageRank paper. Page and Brin themselves acknowledge that (while they were still academics):
[L]ess blatant bias are likely to be tolerated by the market. For example, a search engine could add a small factor to search results from "friendly" companies, and subtract a factor from results from competitors. This type of bias is very difficult to detect but could still have a significant effect on the market. Furthermore, advertising income often provides an incentive to provide poor quality search results. For example, we noticed a major search engine would not return a large airline’s homepage when the airline’s name was given as a query. It so happened that the airline had placed an expensive ad, linked to the query that was its name. A better search engine would not have required this ad, and possibly resulted in the loss of the revenue from the airline to the search engine. In general, it could be argued from the consumer point of view that the better the search engine is, the fewer advertisements will be needed for the consumer to find what they want. This of course erodes the advertising supported business model of the existing search engines. However, there will always be money from advertisers who want a customer to switch products, or have something that is genuinely new. But we believe the issue of advertising causes enough mixed incentives that it is crucial to have a competitive search engine that is transparent and in the academic realm.
For example, a search engine could add a small factor to search results from "friendly" companies, and subtract a factor from results from competitors.
Google absolutely does this - for example, to a site that I own.
So it's not just theory: Google has put it into practice.
In this case, my site is subject to the "subtract a factor from results from competitors", but that's equivalent to Google's preferred site buying rank.
Unless you're talking about AdWords, it is not possible to pay Google in any way to improve the ranking of your site.
This was obvious back when Yahoo, WebSpider (Spidercrawler), AskJeeves, and AltaVista did it.
It was ridiculous that you would type in "Delta Airlines tickets" and the results would go: United Airlines, TWA, Fly By Night Corp, Rickety Rickshaw Airlines, We Barely Stay in the Air, and DuctTape & Flights.
The results were so bad that when Google came along and used the PageRank feature to deliver information, it was a godsend (Thanks God). Try searching for something on Google today and there is a high likelihood that you find or at least get close to it.
Just remembering how bad it was back in the day until the web search engines got their act together and became Bing and Google.
Has Google ever officially stated that they've done away with the old practice of buying rank? The same thing happens now, just unofficially. Employees of Google manipulate its search rankings, even if there is
no "official" way for companies to purchase rank.
[L]ess blatant bias are likely to be tolerated by the market. For example, a search engine could add a small factor to search results from "friendly" companies, and subtract a factor from results from competitors. This type of bias is very difficult to detect but could still have a significant effect on the market. Furthermore, advertising income often provides an incentive to provide poor quality search results. For example, we noticed a major search engine would not return a large airline’s homepage when the airline’s name was given as a query. It so happened that the airline had placed an expensive ad, linked to the query that was its name. A better search engine would not have required this ad, and possibly resulted in the loss of the revenue from the airline to the search engine. In general, it could be argued from the consumer point of view that the better the search engine is, the fewer advertisements will be needed for the consumer to find what they want. This of course erodes the advertising supported business model of the existing search engines. However, there will always be money from advertisers who want a customer to switch products, or have something that is genuinely new. But we believe the issue of advertising causes enough mixed incentives that it is crucial to have a competitive search engine that is transparent and in the academic realm.