What are the strongest arguments against Approval Voting?
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The title says it all.
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As compared to Score{0-10 by 1}, Approval may require more effort to apply the proper strategy/tactic. I think it requires using probability. This is too hard to explain to typical voters. It may be too hard to recruit activists for the system because of false intuition about the system that would be bypassed with Score{0-10 by 1}. People perceive a dilemma about whether to approve compromise candidates, as though the only answers were to approve them always or never, when the correct answer is to approve them with a probability depending on your Score vote for them. If the voter is going to figure out her Score vote, why not use Score{0-10 by 1} voting?
An attempted counterargument may say that Approval is easy to count by hand, but Score {0-10 by 1} would take too long. The counter to that is to say the initial election can be done with computers, the winner placed in office, and a hand check done afterward.
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As said, voters can often face a dilemma of whether to approve someone or not. What counts as approval etc. If I approve my second favourite candidate, what if it turns out my favourite could have won after all?
Also under ranked voting, ranks have less of an obvious meaning so a voter doesn't have to feel they are explicitly endorsing a candidate when they rank them over someone else. Say my preference order is A>B>C and B and C are the frontrunners, but I hate both B and C while preferring B to C. I might happily rank A>B>C. But to explicitly approve B might be a step too far, even though it's the strategically optimal vote for me.
Also, it really invites people to say that it violates one person, one vote, and you have to explain why it doesn't.