The part that I don’t quite follow is about the structure of the Nash equilibrium in the base setup. Is it necessarily the case that at-equilibrium strategies give every voter equal utility?
The mixed strategy at equilibrium seems pretty complicated to me, because e.g. randomly choosing one of 100%A / 100%B / 100%C is defeated by something like 1/6A 5/6B. And I don’t have a good way of naming the actual equilibrium. But maybe we can find a lottery that defeats any strategy that priveliges some of the voters.
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.
The part that I don’t quite follow is about the structure of the Nash equilibrium in the base setup. Is it necessarily the case that at-equilibrium strategies give every voter equal utility?
The mixed strategy at equilibrium seems pretty complicated to me, because e.g. randomly choosing one of 100%A / 100%B / 100%C is defeated by something like 1/6A 5/6B. And I don’t have a good way of naming the actual equilibrium. But maybe we can find a lottery that defeats any strategy that priveliges some of the voters.
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.