This preference situation happens in every election, and approval voting has no answer to it. It's completely unclear what a voter should do to get the result they want.
"What the voter should do to get the result they want" assumes a level of individual agency which really isn't present in a real election: The result is always a combination of individual choice with collective will.
This kind of situation isn't special. It comes up in every election, and approval is completely confused about how to handle it.
I recently had the occasion to really game out what happens in ranked choice voting. It is similar to approval voting (you should only rank people to approve of), but in practice you elect whoever gets past the 50% threshold first, which may not be whoever had the most raw approval. The first person past 50% is effectively random, especially in a large field with complicated voter preferences. So, you get an illusion of choice: everyone lists their preference, but the actual winner is a somewhat random choice amongst the candidates with >50% approval. Thus, I advocate removing the illusion, and simply picking the candidate with the greatest approval. Easy.
http://www.youtube.com/watch?v=JtKAScORevQ
optimal approval voting strategy is simply to approve everyone you prefer to your expected satisfaction. to an approximation it's, "vote for who you normally would, plus everyone you like better." so it's rarely any more taxing than now, and often easier.
hundreds of thousands of voters have now used approval voting in fargo and st louis, and we've heard no reports of difficulty. approval voting is also simpler in essentially every way we can objectively measure. most of the points here apply to approval voting even more so.
https://medium.com/election-science/star-voting-is-simpler-t...
This also is addressed by the point that what you describe is the most complicated part of approval voting. But I'd argue that that is way less of an issue than the current spoiler effects we see in FPTP and RCV, since that is the limit of how complicated your choice can get in practice, whereas with other systems there's much deeper dynamics with respect to tactical voting.
Except that approval voting doesn't allow you to express your preferences very well, since there is very limited differentiation between candidates. I understand the appeal of approval voting since it's a very small change to the voting machines, voter experience, existing legislation, etc, but most people who want to express their preferences will be drawn to methods that actually let you do that most effectively. If approval goes head to head with IRV or STAR (the two other movements that seem to have some momentum) I would generally expect the voters to go with STAR or IRV, for better or worse.
Again, so what? The function being optimized here is not "fealty to true preferences for individuals", but rather "level of satisfaction with outcome for the entire group of electors". And actually, my preference is to not be asked to rank candidates but just issue binary assessments. Your claim that people want the former is wild, unsupported hypothesis, and the way you phrased it seeks to imply they'd rather not vote than vote approval voting. I think you are strongly (albeit transparently) forcing your own preferences through others' mouths in an attempt to start this more or less malformed debate.
> approval goes head to head with IRV or STAR (the two other movements that seem to have some momentum) I would generally expect the voters to go with STAR or IRV, for better or worse.
IRV is literally the same thing as RCV and so displays the same idiosyncracies and fundamental flaws so I'm not quite sure you know what you're talking about here.
Further, the kind of person attracted to STAR is the same kind of person who can devise linear algebra algorithms for deciding what's for lunch, and go in to change every setting on their new smartphone before the wallpaper. They are micromanipulating technocrats, and while this community massively overly represents that type, it doesn't represent the public per se. I assure you, what you parrot from online discussions by people who very much don't have their finger on the pulse, is then predictably very far from representing views considered "normal" in the literal sense.
yes it does, in the aggregate. because the people who approve only X or only Y will statistically have a pretty similar X-vs-Y preference as all other voters (who approved both or neither).
https://medium.com/election-science/expressiveness-6ef8c034b...
and because approval voting uses the preferences it does have more accurately than IRV, it ends up being much more accurate, as measured by voter satisfaction efficiency simulations.