I know you think about candidates in absolute terms while I think relatively.
Not sure what you mean by thinking of candidates in absolute terms. I have always been emphatic that voters should score RELATIVE to the others on the ballot.
I'm not sure I understand your question (or what that has to do with it eliminating the negative effects of vote splitting, which to me is a completely different issue than how you resolve one particular scenario).
Proof by counter example is a perfectly rigorous method for mathematical proof. I pointed out a scenario where negative voting could not encode enough expression to resolve both vote splitting instances on the ballot. You reply by stating that Approval Voting (which I did not mention) will not encode all the information needed to resolve an issue unrelated to vote splitting.
The strategy is very similar to strategy in FPTP, but you've got more options.
Agreed. Vote splitting still exists but it is better than plurality voting.
I think it is common for voters to only have a strong opinion about a single candidate
This is what I was doubting in the last email. I would need some real evidence before I endorsed a system that baked that assumption into it.
I'm highly skeptical that various studies (that by necessity seek to answer very generalized questions) prove anything one way or the other, but I don't really care to debate that at this point.
I agree that it is hard to get a definitive answer. In the absense of a knowing I would stay away from restricting the expression of voters. This comes with a trade off in complexity where the spectrum is something like
plurality - Negative voting -IRV - Approval - Score - STAR
You need to be to the right of IRV to not have vote splitting and that is what I think is the most important.