Do you know of a proportional form of Bucklin voting? What do you think of the Borda count and the Quota Borda system? I believe they're straightforward to tally and sum (at least the single-winner form), and that between them they're suitable for both single-winner and multi-winner elections.
I wonder how important summability is. If voters submit paper ballots, why can't election officials scan them locally and electronically transmit them to a central location for machine counting? Couldn't that make non-summable Condorcet systems work?
> Do you know of a proportional form of Bucklin voting?
Since Bucklin is essentially IRV with the same thresholds and no loser-elimination, the natural proportional generalization would be essentially STV without loser elimination (you'd keep STV’s winner elimination, of course)—and you could, as for STV, use either the Hare or Droop quota.
> I wonder how important summability is. If voters submit paper ballots, why can't election officials scan them locally and electronically transmit them to a central location for machine counting? Couldn't that make non-summable Condorcet systems work?
Sure, they can function in the ideal case; it's harder to audit the results and because the relation between any kind of subset counts or other signals and the ultimate results is somewhat opaque, it's harder to even establish rules as to when you need to do a partial or full independent confirmation. This becomes a concern if you have worries about either internal corruption or external attacks on election integrity. Ballots that can be manually canvassed in public and simply aggregated leave less room to hide shenanigans.
I wonder how important summability is. If voters submit paper ballots, why can't election officials scan them locally and electronically transmit them to a central location for machine counting? Couldn't that make non-summable Condorcet systems work?