Yeah, I’m not actually sure about the equilibrium either. I just noticed that not privileging any voters (i.e. the pure strategy of 1⁄3,1/3,1/3) got beaten by pandering, and by symmetry there’s going to be at least a three-part mixed Nash equilibrium—if you play 1/6A 5/6B, I can beat that with 1/6B 5/6C, which you can then respond to with 1/6C 5/6A, etc.
Yeah, I’m not actually sure about the equilibrium either. I just noticed that not privileging any voters (i.e. the pure strategy of 1⁄3,1/3,1/3) got beaten by pandering, and by symmetry there’s going to be at least a three-part mixed Nash equilibrium—if you play 1/6A 5/6B, I can beat that with 1/6B 5/6C, which you can then respond to with 1/6C 5/6A, etc.