Should runoffs in approval voting include all majority approved candidates?
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When holding an approval vote, which for some (legal) reason requires a runoff. Should it include all candidates approved by a majority of voters?
I started thinking about this as I tried to simplify score interval voting (SIV). The idea behind SIV is to identify possible cases of the chicken dilemma and have those candidates only compete in a second round while excluding the other. By the nature of the chicken dilemma, in most cases there is a majority which prefers some set of candidates to everyone else but is divided about who of those candidates should win. Therefor, it should be possible to avoid the CD (in most cases) if we just take all candidates approved by a majority and advance them to the second round. This isn't a complete fix but should be good enough as a practical approximation.
With this template one could think of several voting methods.
majority approval, with approval runoff:
Approval voting in the first round. The top two candidates and everyone approved by a majority of voters advances to the second round of approval voting.majority approval // score:
Using a score ballot. Every score above 0 is considered an approval. The top two candidates and everyone approved by a majority of voters advances to the second round. The second round is using the same ballot data for score voting.majority score // BTR-score:
Like BTR-score, order the candidates by score and have a bottom-two-runoff until one candidate remains. But limit the set of candidates to all which have more than 50% of the possible score.The idea is related to graded Bucklin methods.
I think the first one is especially useful because of its simplicity. Some places already require an obligatory second round (primary and general in the US). In such cases it's an easy way to address the most common criticisms of approval voting - that you have to think to much about strategy in order to vote. It also addresses the question why you have a runoff after an approval vote with two potentially very similar candidates.
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Isn't the usual legal reason for including a runoff that a "majority" is required? Limiting the count of candidates in the runoff to two-count ensures that one of them will have a majority.
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Yes, but by including everyone approved by a majority, this is already the case. If in the second round people narrow their support, that's the point of the second round.
The wording "the top two most approved candidates and anyone approved by a majority" ensures that there is always a majority. Either in the first round or the second. If there is no majority in the first round then the top two advance and it is like a regular runoff.(It would be possible that a enough people submit an empty ballot in the second round and thereby cause both candidates to fail the majority, but one could count them as invalid - just like in every other runoff.)
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@casimir Ah. Then if that holds up in court, I think the power relations would not be damaged by putting more candidates in the final. The subset of voters who are unwilling to research obscure candidates would benefit from receiving a major hint about what other voters have judged. Candidates receiving majority approval in the primary would seem worth their attending to.