Too bad we don't live in a democracy.
We need to abolish the presidential primaries.
Political parties should be more ideologically coherent (so they can do what they promise) not less ideally, the problem is that the US has completely squeezed everyone into just two parties. A proportional electoral system for Congress and a preferential voting system based on a national popular vote for President would gradually break this down. After centuries of the duopoly, it would take time for people to get used to the new system but this would be a great change to make.
It would ultimately lead to more compromise. It is far more plausible for compromise to occur when the ideological differences are smaller than those between congressional Democrats and Republicans and not ever political incentive is urging them not to compromise.
