Case 2: Joe adds 6 to each vote in Case 1. That raises every candidate's average by the same amount, hence has no effect on the choice of winner.
Case 3: Jane votes 1, 5, and 9. Now Jane has exactly 4 times as much effect as Joe.
The other thing I'm wondering about is how you define the "magical optimum winner" and why Honest Range doesn't select it. If it's defined as "maximum total utility" then Honest Range would.
Re: Erroneously?
Case 2: Joe adds 6 to each vote in Case 1. That raises every candidate's average by the same amount, hence has no effect on the choice of winner.
Case 3: Jane votes 1, 5, and 9. Now Jane has exactly 4 times as much effect as Joe.
The other thing I'm wondering about is how you define the "magical optimum winner" and why Honest Range doesn't select it. If it's defined as "maximum total utility" then Honest Range would.