Coming back to this, it may be the case that you’d consider my examples not too bad for Sequentially Spent Score or for Hamilton more generally. However, philosophically I see Hamilton as the wrong direction to be heading in in the first place, and would consider highest averages/divisor (e.g. D’Hondt or Sainte-Laguë) a far superior starting point. So instead of going with a Hamilton method and arguing that the wrong/weird results it throws up aren’t really that bad, you can cut that out by going straight for highest averages.
With Hamilton, you are building failure of IIA into the system from the start. I’d also question using Hare quotas (or quotas generally) in the way Sequentially Spent Score does. I presume a Hare quota in this case just means 1/s of the maximum possible score for a candidate, where s is the number of seats. In cases where there are lots of voters only giving scores to candidates that have no chance of being elected, the Hare quota and the surplus handling may never come into play. Whereas with exactly the same credible candidates, but no “non-entities”, the quota might be hit more often and the reweighting would be changed and so a different result might come out even with the same credible candidates and the same ratio of support for them.
And this comes back to highest averages vs largest remainder. Under highest averages party list systems, it doesn’t matter if there are smaller irrelevant parties “stealing” the quota, because it’s not used so they pass IIA. Under largest remainder, irrelevant alternatives make a difference because they change the proportion of the quota that the other parties reach.
I understand that vote unitarity came about because you didn’t like RRV’s reweighting system. But I actually think that this was an intuitive dislike and that it is actually wrongheaded. That’s not to say that I like RRV generally, but highest averages methods such as D’Hondt and Sainte-Laguë work by using these divisors, and I would say that they are mathematically correct. So it’s not the divisors that are wrong, but other things that RRV does.
Basically I would struggle to back any system that doesn’t reduce to a highest averages/divisor method for party voting. It’s the basic starting point to build on and that’s the easy part. Getting a voting system to behave in the manner we would like when there isn’t party voting is the hard part. But I don’t see the point in deliberately falling at the first hurdle.
And the final thing I want to say is about the metrics. I would say that the most important thing is to come up with a sensible definition of proportional that works for non-party voting, and find a system that obeys this as well as other basic criteria (or at least fails as little as possible) such as monotonicity, IIA etc. Because if it’s these other metrics you want to optimise, you might not necessarily be chasing a proportional method. So I see them all as a red herring really.
Well, the other consideration that I would take seriously is strategic voting. Basically my idea would be to find the “best” optimising system you can using the criteria of proportionality etc. and then use this as the measure of all systems you’re testing under various strategic assumptions and see which comes out best overall. This “best” system might not win because it might come out poorly by its own measure when voters are strategic and when candidates are elected sequentially.