We have three very different judges in Ivanhoe. First (and least important), Ivanhoe gets to decide who is the prettiest girl at the Ashby-de-la-Zouche tournament. He's like a beauty pageant judge. He is clearly biased, since he goes straight for his childhood sweetheart, Rowena.
Speaking of bias in judgment, we also have Lucas Beaumanoir, the complete tool who tries to use his authority as head of the Knights Templar to condemn Rebecca to death for witchcraft – a totally bogus accusation. Beaumanoir is not at all objective as a judge. He has already decided that Rebecca is guilty before the trial, but he still insists on going through the motions just to pretend that her conviction is fair and just. If it weren't for Bois-Guilbert's weird, sudden stroke on the battlefield during Rebecca's trial by combat, she would literally be toast.
Last but not least we have Robin Hood, with his very own outlaw kingdom in the forests of Sherwood. As the leader of his band of thieves, Robin Hood gets to decide who's right whenever his men disagree. In a sense, even though Robin Hood is literally an outlaw, he is still the best example of a judge that we get in the whole book. He definitely has his own biases, but he tries his best to be fair-minded – which is more than we can say for Lucas Beaumanoir.
By portraying much of the injustice in Ivanhoe as resulting from King Richard's absence from England, the novel makes a case for the importance of a strong, centralized ruler to keep order in the nation.
Ivanhoe argues for nonviolent resolution of social injustice. While there are armed conflicts between the powerful Normans and the rest of the English nation, many of the social problems portrayed in the novel are resolved without violence. For example, Cedric learns to compromise on his anti-Norman prejudices and Lucas Beaumanoir peacefully withdraws his Knights Templar from England.