I'm pretty sure whichever one wasn't picked cursed the city of Troy to die. But what if you answered something ridiculous? Like you said Sisyphus or the Ship of Theseus was the prettiest? What would happen then?
It was the Iliad. As for your answer, Paris was asked specifically by Hera, Aphrodite and Athena (actually, Zeus ordered Paris to do it so he didn't have to) to judge which of the three of them was the most beautiful. His answer had to be one of the three. All three of them were known to be extremely vindictive, so if Paris didn't choose one of them, all three would take vengeance upon him anyway.