Importantly, PageRank doesn't work today - you need something else. It was one of many possible ranking hacks, and one that worked at the particular time in that particular state of the web where nobody was gaming links because PageRank didn't exist yet. Maybe you could invent a good ranking algorithm for the modern internet, perhaps just the reciprocal of the number of ads on the page, minus its AI detector score, but probably not that.

Unimportantly, it's named after Larry Page, not after the fact that it ranks pages.

> Unimportantly, it's named after Larry Page, not after the fact that it ranks pages.

I've always taken it as a happy double play since it is named after Page, but also ranks pages.

Note that Google stopped using it in IIRC 2006.

It wasn't because of the adversarial link farms, though, which are usually handled by trying to identify fake links and take them out of the computation in a preprocessing step. (There are many others parts of Google's '00s ranking algorithm that relied upon backlinks as well). It was because the web scaled to the point where PageRank couldn't process it, because the exact matrix solution to it is O(N^3). They replaced it with an iterative graph traversal algorithm from a set of ~1000 seeds which were themselves chosen through the original PageRank algorithm. I suspect this is published somewhere, because Gemini alludes to it when I ask what's the algorithmic complexity of PageRank.

Interestingly this is a common pattern that Google uses. Come up with a heuristic algorithm that works well enough to get your first million users. Then, train a machine-learned algorithm on the actual behavior of your first million users to scale to your next billion. Assistant's NLP was similar, where the first version had all these linguists hand-inputting grammars for all the different ways you might say a command, and then they just trained a much simpler neural net mapping utterance -> command once they had enough users to get dense training data.

> PageRank doesn't work today

That's silly to say when it can be fruitfully applied in so many situations. Any time you have noisy and sparse pairwise comparisons, you can think of them as one of the sides of the pair vouching for the other side. If you then solve PageRank for the entire graph, you get a somewhat principled global ranking of all items.

I used it recently to construct a top list of books I read a year based only on sloppy pairwise comparisons between them. I've also used it to judge the quality of other relevance algorithms while keeping the human input to a minimum.

I don't know of many alternatives that work better than PageRank under those conditions. Thurstone-type models require dense comparisons, and Elo doesn't fare very well when the comparisons are too noisy.

> Importantly, PageRank doesn't work today

It works as well as it ever did, i.e. in non-adversarial situations. It's not designed to be secure so it fails when people try to game it. Designing something like Page Rank that works in an adversarial environment is still an open problem.

Another Goodhart's Law casualty...

Really?? And not BrinRank?

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