We do a mix of all of these. We do a bunch of discussing, and if it looks like there might be a consensus, that's great and we do with that.
But then when we get to voting, in addition to voting for top choices, we vote "above the line" vs "below the line". Where, roughly above the line means you think they should get an offer either first, or when other people ahead of them turn offers down. "Below the line" means you'd rather not make them an offer, even if others have turned offers down (basically, you'd prefer the search to fail to making an offer to the candidate). But then we'll often do further rounds of discussion after learning opinions about the line.
It's a method for reaching decisions that face little resistance. The method is a bit more flexible than the unanimous decisions that you describe, and it also involves some scoring. The gist is that candidates are scored by how much people oppose them (not how much they like them), and the candidate with least total opposition wins.
Overall, the method to choose depends somewhat on the goal of the process. Are you trying to elect a candidate that everyone likes to work with and who produces good (though not necessarily exceptional) results? Then something like systemic consensing or unanimity might work well. Are you instead looking for the top candidate and wouldn't be satisfied with a second-best? Then you might be better off with approval voting or ranked voting methods.
What you call "Weighted Approval Voting" seems to be called "Score Voting" in the literature. You can find an analysis here: https://electionscience.org/library/score-voting/ The site also has a lot of research on other voting methods.
We do a mix of all of these. We do a bunch of discussing, and if it looks like there might be a consensus, that's great and we do with that.
But then when we get to voting, in addition to voting for top choices, we vote "above the line" vs "below the line". Where, roughly above the line means you think they should get an offer either first, or when other people ahead of them turn offers down. "Below the line" means you'd rather not make them an offer, even if others have turned offers down (basically, you'd prefer the search to fail to making an offer to the candidate). But then we'll often do further rounds of discussion after learning opinions about the line.
Have you looked at "storable votes"?
https://en.wikipedia.org/wiki/Storable_votes
Have you heard of Systemic Consensing? https://en.wikipedia.org/wiki/Systemic_Consensing
It's a method for reaching decisions that face little resistance. The method is a bit more flexible than the unanimous decisions that you describe, and it also involves some scoring. The gist is that candidates are scored by how much people oppose them (not how much they like them), and the candidate with least total opposition wins.
Overall, the method to choose depends somewhat on the goal of the process. Are you trying to elect a candidate that everyone likes to work with and who produces good (though not necessarily exceptional) results? Then something like systemic consensing or unanimity might work well. Are you instead looking for the top candidate and wouldn't be satisfied with a second-best? Then you might be better off with approval voting or ranked voting methods.
What you call "Weighted Approval Voting" seems to be called "Score Voting" in the literature. You can find an analysis here: https://electionscience.org/library/score-voting/ The site also has a lot of research on other voting methods.
I have written about optimal voting systems before (https://paretooptimal.substack.com/p/a-proposal-for-democracy), though not in great detail. I haven't heard of this being suggested outside of public policy, but I suspect quadratic voting (https://en.m.wikipedia.org/wiki/Quadratic_voting) could be a good alternative.
Still, it would be weird to use that for hiring.