It’s the closest thing a hand-countable cardinal PR method can probably get to PR as traditionally defined. It also seems to receive the least opposition from folks who want PR and are concerned cardinal methods won’t transition well to that.
It is not hand countable without a surplus handling system other than fractional. Most I know of are technically hand countable but not practically.
PS I am not a huge fan of the name. It is sort of a technical name.
Here is a trick for hand-counting that should work for any quota-based cardinal PR method: randomly check the quota scores for each candidate until 2 of them have at least 75% of a Hare Quota’s worth of points (in their most-supporting Hare Quota of ballots), then elect the candidate with more points in their quota of ballots.
Which ones are? Random surplus handling?
Apportioned Score Voting (most points wins, unless the Hare Quota of ballots to be apportioned give more points to someone else) should definitely be hand-countable.
Anything with ballot weights becomes very hard to do by hand.
Allocated methods can be done without ballot weights using random allocation, right? Are there any other ways to avoid ballot weights?
That is the big question for allocation. You can find things that allocate based on a rule but that rule may have consequences that are not wanted. For example allocate people where the winner is their first choice first. You will always have to do some random sampling or scaling but a suplus handling method like this can substantially reduce it.
Unless you do not care about immunity to clones, then you can come up with a rule which will always totally distinguished different ballots.