they could make political decisions(ex. building a wall), they could also make religious choices. They could kinda do whatever they wanted.
It's Odysseus and not Ulysses if this is Greek mythology (hence Zeus). That Greek God is Hermes, or Mercury if in Roman mythology (hence ulysses). Use Mercury or Hermes depending if it's Roman or Greek mythology. Determine which one is which as your question mixes the mythologies up.