This question refers to strategic voting, or where voters consider more than just their preferences. Approval Voting has proven to be extremely resistant to strategic voting in both real-world elections and mathematical simulations. This is because in Approval Voting there is no punishment for choosing your preferences. In some cases, you may only have one candidate on the ballot they approve of. In other circumstances, you may notice a candidate that isn’t your favorite, but you also like, is getting a lot of support, and choose to vote for both so you still have a say between the frontrunners in case your favorite does poorly. Whatever the situation, voters can vote their honest preferences.
Additionally, in both real-world elections and opinion polling, voters have consistently approved of multiple candidates. In Fargo, North Dakota, voters used approval voting to select city commissioners. There was an average of 2.3 votes per ballot in a race that would elect two councilors. This was up from 1.8 in the previous election where voters could not select more than 2 candidates. In the St. Louis Mayoral Primary election in 2021, which used approval voting, there was an average of 1.56 votes per ballot, meaning that many voters did approve of multiple candidates. We expect to see this number increase as voters get more familiar with using and watching the results of approval voting.