Runoffs in Approval Voting

If no one has a majority of Approvals, is there any type of runoff built into the system?

TIA

Approval is automatcally a runoff system. The best way to think about it is that STAR with Approval votes gets the same result as plain Approval.

It’s possible to modify runoffs into Approval two ways - either use IRV with equal ranks allowed, and each candidate gets one vote at each rank, or have voters rank the candidates they approve of (even their disapproved candidates, if an approval threshold is included), and between the two most approved candidates, whichever was ranked higher by more voters wins. The former is mostly equivalent to Approval with sequential eliminations until someone has a majority, the latter to Approval + Runoff.

Or just do what St. Louis is going to do and have a separate runoff between the top two.

Not really. Only those voters who approved one but not the other of the top two will have a voice in the “automatic” runoff, making it meaningless. The point of a runoff is to allow all voters to have an equal impact on the final two.

While technically true, for game theoretic reasons the number of people who approve both will be small. There are scenarios where many can disaprove of both.

I wonder if it would work to say to the voters “Rank your choices, but you will be giving your approval to each candidate you list. The rank will be used only if no one has a majority of approvals.”

What about using score ballots and giving approvals to all candidates that the voter rated as 5. If no one got the majority then add approvals to candidates rated as 4 and so on.

Reminds me of Bucklin voting. It would probably make more sense as a ranked-ballot-with-equal-ranks-allowed.

Why not just use STAR?

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Depending on how you resolve ties, you are describing is a median rating based voting method like majority judgement and graduated majority judgement (based on how you describe it by counting one rating at a time it sounds more like graduated majority judgement). Both of these two method are described in this article.

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This seems the simplest way to do something similar to Sequential Monroe (add in ratings from 5 down until someone has a quota of points.)

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Majority of approvals is an arbitrary threshold anyway. Do you only have a run-off if no-one has a majority, or also if more than one has a majority? And then what if it’s three or more?

You could just a have a run-off between the top two anyway if that’s what you wanted.

In a sense, Condorcet is Approval with runoffs; if Approval is considered to be equally ranking candidates as your 1st choice, Condorcet allows for further distinctions and runoffs to determine a winner. However, since runoffs inherently can encourage Favorite Betrayal and Anti-Favorite Betrayal in the first round, you lose some of the unique benefits of Approval Voting; it can make sense to approve your least favorite candidate to give your favorite an easy win in the runoff, for example, so it might make sense to separate out some uses for cardinal methods from other uses for runoffs and Condorcet.

Interestingly, it’s also possible to consider the use of Approval or Score in the runoff; a voter might want to give both candidates a vote, or give one of them half a vote (5 out of 10) rather than a full vote, etc. A form of this idea can be used in conjunction with Condorcet: A way to combine scoring and ranking