Two-stage Approval
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Condorcet systems may be too complex to tally during a period of mistrust; that question is under discussion elsewhere.
I want to suggest a framework (for a single winner) where there would be two stages of tallying. Each stage would derive effective Approval ballots from the actual ballots by some rule. The first stage would pass some number of top-approved candidates to the second stage.
Given this framework, what form of ballot would you want, and how would the effective Approval ballots be derived from it?
IRV says that if your favorite is in the running, you support her over all others. Let's permit that, while removing IRV's incentive to invert ranks.
Let an ordinary voter express special support for his favorite candidate and weak support for another candidate. Then in each stage, if the voter's special candidate is in the running, the effective Approval ballot calculated for this voter votes up the specially supported candidate only. But otherwise, the weakly supported candidate gets an up-vote.
This can be extended to allow special and weak support for more (or fewer) candidates. The trip rule would apply if any of the specially supported candidates is still in the running for the round.
To allow balance for a class of voters I think probably unusual, allow special opposition to candidates instead of special support. In this case, the trip rule would trip if any of the specially opposed candidates were in the running for the round. In this case, the effective Approval ballot would not up-vote the specially opposed candidates and would up-vote the candidates not specially opposed.
It should be forbidden to support some candidates specially and oppose others specially.
How many candidates should be in the second stage? One answer is about 1/3 of the initial field, but at least two individuals.