The Byzantines Emperors passed down the title of Emperor to his eldest child as most kingdoms did at the time, but with a twist. You see, if the heir was corrupt or didn't have the best interest for his people the Byzantines could prevent them from becoming Emperor. At all the Byzantine coronations the army, the regular citizens, the church, and the senate had to voice their approval of the heir before he/she could lead them. If the heir did not get the full approval of the people the heir's most close relative would become Emperor. This safeguard prevented some openly corrupt people from becoming Emperor, however if they hid their corruption or became corrupted by the power of being a Emperor, it usually came to blows.
Despite it's flaws, I think this is the best form of monarchy the middle ages ever produced.
What do you think?