Make it an all day event. Jerry Lewis telethon style. Have debate run offs with call in voting. Final two survivors at the end of the day face each other in gladatorial combat.
Once everyone is dead or demoralized, the population can get on about their business knowing that anyone who actually would WANT the job of ruling over millions of people has been safely kept from doing so.
Draw straws. One candidate outfitted in full armor with a short dagger - the other nude with a long sword.