I'd rather separate starred from sponsored. If I could select a subset of that 771 and say "split $10 among these projects" then I'd be happy.
I think it'd be a reasonable default for most people to start with though.
Perhaps offering the projects that you `watch` a higher priority than those you've starred would be a fairer default?
I could see having some kind of "tip amount" per project that gets taken from a pool would make a lot of sense, but not as stars.
Using stars as a proxy for sponsorship, I think, is the wrong idea anyhow. Sponsorship should imply star, but not the inverse. I think what would be best is an easy way to sift through your starred projects and "upgrade" them to a sponsorship. Then once you've done that once, you can manage stars and sponsorships independently going forward.
It would be very cool if there was an easy way to sponsor all the projects I've starred. Then I could just pay (say) $10 per month to "support open source", without having to worry about any of the details such as picking projects. If you as GitHub then also reach out to the project maintainers and say "hey, there's someone who'd sponsor you", then I feel this could significantly increase the uptake of this feature on both the sponsor and the maintainer side.
[1]: https://news.ycombinator.com/item?id=19990110