The median voter theorem isn't the whole story, not even close. In particular, it assumes that most of voters are driven by what parties say about themselves in

The median voter theorem isn't the whole story, not even close. In particular, it assumes that most of voters are driven by what parties say about themselves in terms of policy, which is manifestly not true. When Trump says he won't cut social security, people from deep republican states say "yeah he cares about the american people, he's with the little guy", whereas when a democrat says the same thing they go "boo he wants to social medicine, commie". There was this study that showed when remove parties from policies, something like 90% of the population wants free health care for all, free education for all, richer people to be taxed more, not less. 90% isn't really split down the middle.