Does Ubuntu have an equivalent to the AUR (Arch User Repository)?
Yes, PPAs. That's the closest you can get right now. If you don't think they're equivalent enough for you, then the answer right now is simply "no". Some comments on your claimed differences:
PPAs have compiled packages, while the AUR features both compiled packages and source packages
PPAs ship source packages too. PPA uploads must be source uploads. Users can access both the source (for example they can rebuild the sources themselves), or binaries built from those sources.
Since PPAs are specific to the Ubuntu release, many PPAs are out of date.
This is true. However, users can quite easily copy a package from any PPA to their own PPAs, including to a different release, while choosing to rebuild them if necessary on the way. See the Package details -> Copy packages page. If there is anything that needs updating to work with a newer release then that won't work, but I presume that's the same with AUR.
In terms of PPAs being up to date, that is presumably simply a matter of volunteer time (who can do the same pocket copy as above), rather than any fundamental difference between PPAs and AUR.
Many PPAs don't build properly, even though the projects are more or less stable
Same answer as above. This has nothing to do with infrastructure or mechanism and everything to do with volunteer time.
PPAs don't seem have a rating system where users can vouch for working package repositories.
Agreed.
There are tons of AUR packages that come directly from GitHub, so installing a package like something-git will usually give you the latest package straight from GitHub.
You could arrange for this to happen automatically in a PPA, but I admit it is far from trivial to set up.
- Arrange for an automated VCS import from Github.
- Create a build recipe.
None of this is exactly the same, I'll grant you. If you want more ABS/AUR -like functionality in Ubuntu, I think you need to go into more detail of how exactly your proposed changes would work in terms of what Ubuntu already has.