That doesn't make sense. Your ballot can NEVER express your actual preferences except in a statistical sense—we can have some probability distribution for the a

That doesn't make sense. Your ballot can NEVER express your actual preferences except in a statistical sense—we can have some probability distribution for the actual preferences that created that Approval ballot. Thus using the standard strategy I mentioned is the most accurate way to convey your preferences. If you want them to appear as honest as possible, you just treat all candidates as equally likely to win, such that the formula simplifies down to your approval threshold being "average utility of all candidates".