Tribunes, I thank you: and this suit I make,
That you create your emperor's eldest son,
Lord Saturnine; whose virtues will, I hope,
Reflect on Rome as Titan's rays on earth,
And ripen justice in this commonweal:
Then, if you will elect by my advice,
Crown him and say 'Long live our emperor!' (1.1.10)
Uh oh, big mistake. Titus chooses Saturninus (even though he has just threatened Titus's life) to lead Rome because he is the late emperor's eldest son. What's interesting is that Titus has chosen the emperor according to the rules of primogeniture (the system by which eldest sons inherited their fathers' titles and wealth) and not by any kind of merit-based system. Titus says he "hopes" Saturninus will be a virtuous ruler, but we all know that doesn't turn out to be true. So, the play is very interested in how rulers should be chosen.
History snack: When Shakespeare wrote Titus, primogeniture was the mode by which crowns were passed on when kings died. Obviously, in Titus's Rome, the empery is decided by election, not primogeniture. But the fact that Titus chooses Saturninus over Bassianus suggests that Titus is a traditionalist.