"If you were to design a political system for a representative democracy that would produce a multi-party system with coalition governments, what form of electoral process would you choose?"

Proportional representation

Explanation:

If I wanted to design a political system for a representative democracy that would result in a multi-party system with coalition governments, I would personally go for a system of proportional representation. Proportional representation is a system in which divisions in the electorate are accurately reflected proportionately in the elected body. Because of this, smaller parties are more likely to be able to place elected officials in power. Moreover, this system tends to have a great plurality of ideologies represented in government.