Republics without elections?

When I first came across the Wikipedia article about Demarchy (accidentally) I thought it was some sort of joke... I mean who would want important decisions (like who your representative to the legislature would be) left to random chance right? Here's a quick quote for those too lazy to click on that link:

Demarchy or lottocracy is a political system run by randomly selected decision makers who have been selected by lot.

Sounds absurd and untried right?

Wrong! Life and death decisions are made by randomly selected people every single day, and this has been going on for quite a long period of time without major glitches.

An example of demarchy in most democracies is the use of a jury of peers in criminal cases. The jury is normally a body of randomly selected citizens who decide the guilty or not guilty verdict, which is a prime example of demarchy.

One of the things I found really interesting is that Demarchy effectively ends partisan politics, the single most despised thing about democracies (and also end the enormous wastage of funds that goes into election campaigns as well as the process of holding elections and counting votes).

I'm not going to go on about Demarchy, because it has never been implemented as a system of government, but what would your reaction be if there was a proposal to make your elected representative, well, not 'elected' anymore? :)