The EU uses the ‘d’Hondt method’ which is a mathematical formula for proportional representation systems.

This is the opposite of the US senate.

It’s important to note that there’s no distinction between a democracy and a republic: a republic just is a type of (representative) democracy.

The United States is a republic, true, but there are aspects of our government that are undemocratic and vulnerable to corruption. The Senate is one of these aspects. The Supreme Court is another, so is the electoral college, and the influence of money, and the enormous power of the chief executive.