Jameson Quinn wrote:
If you're looking for simple proportional systems, you could look at "total representation", where district-based representatives win with a majority, but some extra seats are assigned to the highest-vote-getting losers of underrepresented parties to help balance.

I believe that SAV is not that great a system. It requires too much strategy from the voters; you have to know how many voters like you there are in order to know how much to split up your vote. A faction which spread its vote to thin could end up entirely unrepresented - even if it were a majority faction.

> I would propose SPA (Summable Proportional Approval) voting.

[...]

The math is complicated. However, it's only to make the process summable, and thus to make recounts verifiable. If you don't need summability, you just reweight the individual ballots to deduct a Droop quota, which is trivial mathematically.

Hm, that's an interesting approach. The problems of reweighting
a weighted positional system doesn't appear in your method as there are just two levels - approved and not (somewhat like Plurality in that respect).

Does SPA meet the following criterion?

"If more than k Droop quotas approve of p candidates, then at least min(k,p) of these candidates must be elected".

(I'm not sure if it can be met, but it seems like a reasonable Approval extension of the Droop proportionality criterion)

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