Ah! I had a total brain fart and was still scoring the ballots like STAR — "in an election between A and J, A has 4 points and J has 3". -.-

> a condorcet winner can be chosen

A condorcet winner doesn't exist, if there is a circular relationship:

Voter 1: A > B > C
Voter 2: B > C > A
Voter 3: C > A > B

Yes, there are cases when STAR does not elect the condorcet winner. Of course, you could always add condorcet on top, and use STAR as the fallback. But you can do that for any system — basically all of which fail to elect the condorcet winner in some edge case — so it's not a particularly interesting insight. It's more about tradeoffs and what scenarios are most likely.

Note that Approval voting is also a form of score voting — with a range of 0-1. The drawback here is limited expression — I can't say that I love or hate a candidate, and so it can elect a candidate with broad, weak approval and some strong opposition, over a candidate with broad, weak disapproval and some strong support. For example, let's draw the "I approve" line between 2 and 3 stars (approval indicated with +/-):

Voter 1:
5 for A (+)
3 for B (+)
Voter 2:
5 for A (+)
3 for B (+)
Voter 3:
3 for B (+)
2 for A (-)
Voter 4:
2 for A (-)
1 for B (-)
Voter 5:
2 for A (-)
1 for B (-)

A is preferred by 4 out of 5 voters and 16 vs 11 stars, but B wins with 3 approvals, to A's 2.

This is not a terrible failure mode — electing a mediocre, likely moderate, candidate over a decent one — considering it is the worst-case scenario for approval voting. Compare to the worst case scenario for FPTP, where sufficiently many candidates representing the most popular viewpoints split the vote, giving the win to a universally disliked, radical candidate. Of course, in actual elections we (the electorate) avoid this scenario by favorite betrayal, which has its own obvious shortcomings. To fix the Approval voting failure mode, scenario, we just have to be more stringent with our votes (ie, raise our standards).

Note how we were able to use the STAR ballot to derive what the outcome would have been in Approval. If we only had access to the Approval ballot, we couldn't tell that it was electing an inferior candidate. If the goal of the election is to choose the candidate who best reflects the preferences of the electorate, Approval is leaving information about those preferences on the table (edit: as is condorcet!). Aside: I remember reading (maybe on https://rangevoting.net ?) that increasing the range past about 7 sees quickly diminishing returns on this front.

STAR is more expressive, at the price of (mostly) complexity. edit: forgot to add that, while score voting is about the best you can do in terms of preferences among candidates, support of a candidate doesn't capture the full picture, either, since it bundles all the issues you may care about into a single decision (but putting that on the ballot moves us towards a different system of government).

At the end of the day, any form of score voting would be a MASSIVE improvement over the status quo. I would wholeheartedly support any of Approval, STAR, or vanilla score voting (on the same 5-point scale / STAR minus the runoff). I think we should put our efforts behind whichever one is most politically viable. STAR actually has a chance of being implemented (in Eugene, Oregon — see https://www.starvoting.us/campaigns); not sure where Approval stands.