There are basically two types of Democratic-Republics in the world – Parliamentary, or a Prime Minister led government, and a strong President based system. Hybrids of various kinds involving monarchs and other systems with varying degrees of power abound, but every democratically elected government in the world falls into one of these categories. The person who shows up at the international conferences has one of these titles.
But is that the only way to go? The situation in Egypt, among other places, has led me to wonder if there is some way a nation with a history and tradition of strong leadership might do better under a system of more than one nationally elected leader with defined roles and a real balance of power between them. I call it an “Elected Cabinet”, and the inspiration comes from the laboratories of democracy, the US States.