@zeb: The UK does indeed have a different voting procedure, but the government is not obliged to follow the will of the people. Legally, the Queen/King and Parliament/House can overturn a popular vote as we've seen with Brexit.
The US model was an attempt at repairing the flaws in the UK democratic model, no taxation without representation and all that. Hence why the US has a Republic model where every 'community' (county and/or state) is entitled to a vote/seat regardless of its size and population. This was done so the farmers, slaves and poor people that live "in the country" are still represented even though they don't make up the same numbers as the rich people in the city do.
America always appears to be in a flux due to the two-party system controlling the 3 main parts of law-passing government (house, senate and president) but it's also very stable politically speaking because you need compromise between those 3 parties to get any law passed. In comparison, the House of Commons and House of Lords model is a lot more direct democracy so the ruling party gets things passed regardless of how good or bad the thing is and everyone else just deals with it, if May hadn't broken the House of Commons by calling an early election, she would've gotten her shitty deal through and effectively kept the UK in the EU and even so, the Queen can just wave her little hands and do whatever she wants.
Having coalition governments across multiple competing parties like other European countries has also proved to be very unstable in the long term, the current crisis in the UK is one effect but Belgium hasn't had a functioning government for the majority of time over the last decade. Those things don't create trust amongst businesses so they don't take risk, they don't invest, they don't hire.