So it sounds like you're trying to strategically vote to push a party you want in another direction. I totally understand this, but under score or star (where we have more resolution that approval) it is very easy to just extract this information out of an honest ballot. You can measure the distance between the voters and other candidates as well as the distance between your mean voter and other candidates. You have full information about which direction you should alter your course to better serve your population. Approval gives you this information too, it is just not as fine grained. My main (long) post in the thread argues that the advantage of cardinal systems is its ability to effectively embed voter preference better. What I'm talking about here is just extracting that information and that candidates can utilize that information without ever relying on voters to vote strategically.