First off, GrapeRank (GP) should only be compared to Personalized Pagerank (PP). Both are personalized, or "local".
Second, I very much disagree that PP is about popularity. It depends on the graph it is run. If you would "run it on zaps", you would get something that is closer to "value" than "popularity".
Third, the mathematical properties of GP are unknown (does it converge? what's the relationship with distance? what's the relationship with flux? is it graph stable?), but I would they are not promising. Here for example:

Npubs that are 2 and 3 hops from the user, span the whole spectrum of possible values. This suggests that distance DOES NOT really play a role in GP. But distance is something the user can influence directly, by following/unfollowing!
Compare it to Personalized Pagerank where distance actually has both a theoretical and measurable impact. As you can see, the tendency is that, the furthest you go, the lower the score.

Why make this into a competition? We can just have both and people can use what they want.
sure. I am just skeptical of "too good to be true" algos, with no proofs
Why is it "too good to be true"? In my understanding, it's solving an entirely different problem. And when you accept the bounds of its problem and solution then it doesn't seem "too good" it seems "appropriate for the problem"
Correct. I am not claiming GR to be “too good to be true.”
I would counter that PageRank is likewise not “too good to be true.” It’s famous but that doesn’t mean we should blindly accept it as the only tool in our arsenal.
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What are the two distinct problems GP and PP are solving? Genuine question
If your goal is to put pubkeys in order, PR and GR can both serve that purpose in a meaningful way. May as well do the one that is easier to calculate.
If your goal is to do anything that requires a pubkey-specific WEIGHT, such as tallying votes or doing a weighted average, GrapeRank is better than PageRank because PR is inherently a popularity contest, and most of us don’t want weight to be proportional to popularity. Most of us want weights to be proportional to merit or quality, in the relevant context.
GrapeRank is inherently designed to create contextual scores. One context might be designed to distinguish real users from bots, ie a binary outcome (this is the GR score currently available on my site). Another context (I have not yet implemented on my site) might be designed to reflect a pubkey’s expertise in some topic on a scale from min to max. Either of these scores are suitable to be used as the pubkey’s weight in the relevant context.
It’s not clear to me how to do this with classical PageRank. Unless you modify it, of course.
The subjective nature is key here.
My idea of pubkey N's expertise in X may be different than your idea of pubkey's N expertise. We should see pubkeyN ordered differently as a result.
This solves a ridiculous number of societal problems!
Absolutely! The Grapevine is designed specifically to reflect the values and beliefs of YOU, the end user.
If you trust zaps more than follows, or vice versa, then adjust the relevant weights accordingly. The community will need a developer to write the script to ingest follows and zaps into the GrapeRank system, but once that’s done, the average user (who is not necessarily a skilled developer) will have the power to customize his or her Grapevine according to his or her values and beliefs.
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The average GR score decreases as hops increases, as it does with PageRank. Distance plays a role with both.
The average does, but the variance is really high
A high variance does not imply GR is not useful. I’d argue the opposite: it implies the GR score conveys information that is not conveyed by the DoS score alone.
A low variance (tight correlation) between the PR score and the DoS score would imply we may as well just scrap PR and use the DoS score which is easier to calculate. Although I don’t think the correlation is tight enough to suggest we should do that.
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