Sure, thanks, I can see how it can happen now, and actually it revealed my understanding of preferential voting wasn't entirely correct. As for "favorite betrayal criterion" - I actually think it's a feature of preferential voting that I actually take advantage of, whereby I vote [1] for a minor candidate who has policies I agree with but I accept is not in a realistic position to govern effectively (due to lack of experience/resources etc.), but [2] for the party that I'm happy to actually win, providing they're aware they're relying on 2nd preference votes from another party that they can't just ignore.

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.