I believe that a combination of meritocratic principles with the leadership and stability of a monarchy would be an ideal form of government. A meritocracy is an organization (in this form a government) where advancement is based purely on merit. Basically its a system where advancement and rewards are directly linked to the quality of your performance in relation to the state. Leadership for the position of Monarch could be chosen from the pool of talented and proven individuals who have managed to make their way to the top. Perhaps a convention of the highest merited individuals could choose one from amongst themselves.

There is also a historical basis for an elected monarch. In the Holy Roman Empire (the German one) the Emperor was elected from among the nobility of the land.