Question: This global-spanning empire is divided among five royal families, each headed by a prince. The emperor himself leads the empire, with the five princes serving under him. While they owe fealty to the king who has absolute authority over the empire, these families operate semi-independently and control their realms directly, as well as their own security forces and economy. The king holds all secular power by law. However, his right to rule is given to him by the gods, with priests of the theocracy speaking on their behalf.

The selection process of becoming king is administered by the priests themselves in order to prove the future king's worthiness. A series of trials are conducted in which the heads of the five families compete against each other. These contests vary with each selection process, and these princes can participate themselves or elect a champion from their realm to compete on their behalf. The winning prince of these contests is then elected to the position of emperor, and rules until he dies. The four losing princes are ritually sacrificed to the gods. This system is meant to prevent any disputes between rival families as to who is the rightful ruler, and to keep the empire stable.

However, it is possible that a prince or several princes may simply not accept the results. They may lead their families into open rebellion to avoid their honorable fate of being sacrificed for the good of the empire. This is unacceptable, for it would tear the empire apart with various wars.

How would I prevent this from happening?

Answer: 
If I remember correctly, in ancient Japan all the daiymios had to send their sons to reside in the Shogun's castle, where they were held as hostages, as a warranty for the underling's fidelity. The practice was called [Sankin-kotai](https://en.wikipedia.org/wiki/Sankin-kotai), thanks to Jay Carr for pointing to the reference.

The emperor can use a similar system. Each family has to give their heirs into the complete control of the emperor. Rebelling to the emperor and his designation results into the beheading of the family itself, as all of the heirs will face death.

Be faithful and you lose just one member. Betray, and you lose all your descendants.
Make it so each prince can command their own army, but the army they command is at an opposite end of the empire from the lands they actually control. This, while confusing, prevents any prince from consolidating military power in their home territory and using it against the emperor.