From 1268 the oligarcial Venetian republic used a multi-round system of elections and selections by lot to choose the Doge. Apparently that system actually had

From 1268 the oligarcial Venetian republic used a multi-round system of elections and selections by lot to choose the Doge. Apparently that system actually had a lot going for it https://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.pdf https://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.pdf , and the fact that it and the Venetian republic endured for over 500 years after 1268 seems to support that idea. So this is probably the sort of model the US should be seriously considering to reform its somewhat broken electoral/political system, and specifically how it appoints its chief executive. It's discouraging that instead the only systems which seem to have any support or awareness are fully direct election and the system of (weighted-but-otherwise-)effectively-direct election which is already in place.