*Puts on Conan glasses and rubs chin* It doesn't make sense for Irvine to attack Stewart. If Irvine was aiming to be King, he wouldn't have voted for Stewart to begin with. If Irvine was betraying Stewart and aiming to make Cyan or Fran the next ruler, he would have kept his vote blank instead of locking in Stewart to begin with. Plus, he's the Captain of the Knights and is very attached to his men, and doing something like this would obviously forfeit his position.
So what we know so far: All the candidates are blood related to the King. Stewart is the previous King's youngest son, making him eligible for succession. Cyan's father was the King's son (older brother to Stewart) but he passed away, making Cyan eligible for succession, but his mother is not (thus trying to manipulate her son into taking the throne). I think Fran's mother is the previous King's daughter (since Fran's last name is Elliot and Stewart's last name is McTeill) so I think she either waived her right of succession or isn't eligible because she married the Duke.
That leaves Irvine, who is the King's nephew, who is also a successor. Irvine's mother or father is the sibling to the King (most likely mother since Irvine's last name is different from Stewart), but for some reason they're not one of the candidates. They haven't been revealed yet, but back in chapter 3, Irvine mentions that he was listless from being part of the royal family.
So I think it's a good assumption to say that, like Cyan, Irvine is being framed or punished by his own family. I think the culprit who attacked Stewart is *points finger* Irvine's parents!