[jamesonquinn]

The "favorite betrayal" criterion is defined mathematically. In your scenario, as long as you approve Ideal, you are not betraying your favorite, even if you also approve Good. The only betrayal would be if you didn't approve Ideal. And in approval voting, there is no way others could be voting so that betrayal would be a good idea.

You are talking about a form of strategic voting — whether or not you approve Good. But it isn't favorite betrayal. In fact, it isn't betrayal at any level. All rational approval strategy (assuming a convex distribution over others' votes) is "semi-honest" in that you never approve a less-liked candidate but not a more-liked one. The only strategic choice is where to set your threshold, then honestly approve all candidates above it.

According to the Gibbard-Satterthwaite theorem, any voting method has some form of strategy, so in that sense the best you can possibly do is ensure that all strategy is semi-honest. Approval is optimal in this sense.