Evidence suggests that about 30% of people will accept being worse off in order to inflict a greater loss on someone else. They form a plurality, with the other groups being win-win types (~20%), loss-averse pessimists (~20%), selfless volunteers (~15%), and inconsistent folks who may be confused (~15%).
Now this is just empirical observation rather than proof, but it's a good quality observation, enough that it has heuristic value. If you admit the possibility that about 1/3 of people are mean, then an awful lot of ongoing political phenomena become much easier to understand.