Of course Caspian's ship was not that horrible thing, a galley rowed by slaves. Oars were used only when wind failed or for getting in and out of harbour and everyone (except Reepicheep whose legs were too short) had often taken a turn. (2.43)
Narnia may not be a democracy, but it does have principles of equality. Everyone on the ship, from the king down to the lowliest crewman, takes his turn doing hard labor to keep everything moving. Hey, maybe the Dawn Treader is a metaphor for or tiny version of the country of Narnia itself.
There was not much difficulty in settling the matter once Eustace realised that everyone took the idea of a duel quite seriously and heard Caspian offering to lend him a sword, and Drinian and Edmund discussing whether he ought to be handicapped in some way to make up for his being so much bigger than Reepicheep. (2.68)
Reepicheep's desire to duel is one of the most obvious signs of a medieval code of honor in the world of Narnia.
"Your Majesty's tender years," said Gumpas, with what was meant to be a fatherly smile, "hardly make it possible that you should understand the economic problem involved. I have statistics, I have graphs, I have – "
"Tender as my years may be," said Caspian, "I believe I understand the slave trade from within quite as well as your Sufficiency. And I do not see that it brings into the islands meat or bread or beer or wine or timber or cabbages or books or instruments of music or horses or armour or anything else worth having. But whether it does or not, it must be stopped."
"But that would be putting the clock back," gasped the Governor. "Have you no idea of progress, of development?"
"I have seen them both in an egg," said Caspian. "We call it Going bad in Narnia. This trade must stop." (4.25-28)
Caspian's straightforward ethical principle that "slavery is wrong" prevents him from being confused by Governor Gumpas's sophistry, or false logic. In the world of Narnia, most important moral issues boil down to very simple principles, and it's always wrong to compromise anything in order to get something done, make somebody happy, or bargain for something else. Caspian argues that the slave trade isn't necessary or useful for the Lone Islands, but even if it were, he'd abolish it anyway because it's wrong.
"And then Caspian showed up in his true colours as a brutal tyrant and said out loud for everyone to hear that anyone found "stealing" water in future would "get two dozen." I didn't know what this meant till Edmund explained it to me. It comes in the sort of books those Pevensie kids read.
"After this cowardly threat Caspian changed his tune and started being patronising. Said he was sorry for me and that everyone felt just as feverish as I did and we must all make the best of it, etc. etc." (5.13-14)
When the Dawn Treader runs low on water, everyone suffers alike. Eustace's attempt to steal a little extra water for himself is immediately punished because it suggests that he sees himself as superior to others on the ship. Maybe Narnia is more about equality than we thought!
"That's all right," said Edmund. "Between ourselves, you haven't been as bad as I was on my first trip to Narnia. You were only an ass, but I was a traitor." (7.54)
Eustace may be irritating, but he's not immoral.
"Her Majesty is in the right," said Reepicheep. "If we had any assurance of saving her by battle, our duty would be very plain. It appears to me that we have none. And the service they ask of her is in no way contrary to her Majesty's honour, but a noble and heroical act. If the Queen's heart moves her to risk the magician, I will not speak against it." (9.79)
Everyone is surprised when Reepicheep argues that it's ethical for a group of strong, powerful men to let a little girl take a serious risk on her own. However, as Reepicheep points out, some risks are honorable. Lucy may be in danger, but it's an acceptable kind of danger.
"Spying on people by magic is the same as spying on them in any other way." (10.47)
Supernatural elements may make the world of Narnia more exciting than the "real" world, but they don't change fundamental moral rules.
"Sometimes, perhaps, I am a little impatient, waiting for the day when they can be governed by wisdom instead of this rough magic." (11.4)
Coriarkin would prefer to run his island according to reason, explaining his decisions to his subjects, but he and Aslan both know that his subjects need to be dominated and controlled with magic for now. The Dufflepuds don't know what's good for them.
"It's better for them to admire him than to admire nobody." (11.25)
Celebrating heroes is a valuable activity in its own right, even when the heroes may not be completely worthy of admiration. The effect on us of feeling admiration and looking up to heroes is morally beneficial, even when the heroes themselves make mistakes.
"My son," said the star, "it would be no use, even though you wished it, to sail for the World's End with men unwilling or men deceived. That is not have great unenchantments are achieved. They must know where they go and why." (14.27)
Caspian is a king, but he's not supposed to be a tyrant. As Ramandu reminds him, he governs with the consent of his subjects – especially when it comes to dangerous adventures!