This personality article is an opinion by a fan and should not be considered canon.
Edmund is quite popularly known to have the most complex personality of all the protagonists and to be one of the few rounded characters, whose personality changes and develops during the series. He is also considered to be one of the most popular characters, if not the most popular, especially due to his depth and dark side that he still keeps, even after his redemption.
As observed from the very beginning, Edmund has a great need for attention and glory, though less so after his experience with the White Witch. The idea of being better than others is what makes Edmund bully Lucy early on. He likes it when the Witch calls him clever, and he loves the idea of being king. Edmund also likes to seem smart, making high-and-mighty, “educational” remarks about Fauns and little children.
In Prince Caspian, Trumpkin doubts that Edmund and his siblings are kings, queens, and warriors. According to the book, Edmund gets red in the face and does not calm down until both Peter and Lucy tell him to. Even after Trumpkin is their friend, Edmund is a little sarcastic about him.
On Goldwater Island, in The Voyage of the Dawn Treader, Edmund almost comes to the point of fighting Caspian over who shall name the newly discovered island. Edmund argues that he should name it because his brother, Peter, was High King. In the film, he is tempted by the White Witch who promises him power, and on Goldwater Island he fights with Caspian because he wants to use the pool to get power. He also says that both Peter and Caspian have made him the second best and put him down. All of these examples show that Edmund is afraid he's worthless.
According to The Lion, the Witch and the Wardrobe, he feels so bad about himself that he imagines his whole family is giving him the cold shoulder. Edmund then felt the need to get them all back for their unfairness. With that in mind, it is clear why his experience with Aslan changed him so drastically. To the Great Lion, Edmund was just a lost lamb with the makings of a Great Leader: and he treated him as such. Aslan treated Edmund With love and acceptance. Finally feeling like he was worth something, Edmund became a better person.
One of the most memorable traits about Edmund is his intelligence. It is his sensible idea to break Jadis' Wand, and without that idea the battle of Beruna may not have been so successful.
Edmund presents logical arguments of why the ruins cannot be Cair Paravel when he returns to it in Prince Caspian. Despite this, it is Edmund who figures out about the time gap between his world and the Narnian world. According to Voyage of the Dawn Treader, Edmund likes reading detective stories, and figures out the death of a Narnian Lord on Goldwater Island. He apparently knows some things about Greek lore too, as he compares Caspian X to Ulysses.
Edmund's intuitive nature and sense of caution can be seen back in The Lion, The Witch, and The Wardrobe. Although he likes attention, Edmund feels uncomfortable around the White Witch. According to the book, he knows she's on the wrong side. Edmund does not trust the Robin that leads them, and suggests to Peter that they could get lost.
In Prince Caspian it is Edmund's idea to take the Glasswater route, but once the way becomes unfamiliar, he suggested they do not continue. Peter decides to press on. In The Voyage of the Dawn Treader, Ed has the idea to test the pool on Goldwater Island. He also questions whether or not to trust Ramandu's daughter. In addition, Edmund points out that if the Narnian world is flat, they could all be pulled over the edge of it. Furthermore, Edmund points out that he does not trust Prince Rabadash in The Horse and His Boy.
As for Edmund's sense of humor, it is mostly sarcastic. He makes many sarcastic and perhaps embittered remarks during The Lion, The Witch, and the Wardrobe. He makes a joke about Lucy and imaginary worlds; it is Edmund's first reaction to laugh at Professor Kirke. In Prince Caspian, Edmund's lines concerning Algebra and lunch are humorous, if unintentionally so. He later treats Trumpkin with sarcasm. When Susan says that the Glasswater route was a blessing in disguise, Edmund says, “Some disguise!”
In Voyage of the Dawn Treader, Edmund's early observations about Eustace are quite amusing.
Edmund becomes Lucy's greatest supporter later on in the series, and he becomes the one who looks after her the most, especially when they are sent away to an unwelcoming place, to their ignorant, uncaring relatives. Edmund and Lucy become perhaps the closest siblings of the main four, and probably have the most complex relationship of all the characters, a relationship that evolves the most, from bullying and taunting from Edmund's side, to protectiveness and care for Lucy.
Lucy is the one who brings Edmund to his senses when he loses his self-control or when he is tempted by evil, as seen in the third movie, where she constantly stops him from using violence on Eustace, and snaps him out of his evil self after he's tempted by the magic pond. She also distracts him every time he has illusions of the White Witch. Edmund is also very practical, as he seems to possess a keen awareness of his senses.
Edmund seems to have a more cold-natured thinking, a sharp mind and logic. He is rarely driven by emotions and is mostly a collected and down-to-earth person, having an acute sense of justice, going to the point where he becomes unsympathetic towards enemies and downright cruel, as opposed to Peter, who is more impulsive and emotional. This is proven when Peter battles Miraz, because Edmund tells Peter not to be chivalrous, and to strike Miraz. The scene suggests that, if Edmund had been in Peter's place, he would not have hesitated and would have killed Miraz in a heartbeat.
Edmund loves good food, especially Turkish Delight, and points out once all four siblings are in Narnia that they have no way of getting supper. He is conscious of the smell of camphor, and the feel of the snow and coats when entering Narnia.
When the siblings are all hungry on the island in Prince Caspian, it is Edmund's idea to go into the woods and look for food. When Lucy sees Aslan in “Prince Caspian,” Edmund asks why Aslan is invisible, or how Lucy even knows he's there. Edmund is also very navigationally aware, as in The Lion, The Witch and The Wardrobe, he points out that they need to bear more to the left if they want to find the Lamp Post. “In Prince Caspian”, Edmund reminds Peter of his compass and directions. He also makes a sarcastic remark because Susan cannot remember any navigational information. In addition to this, Edmund's memory of the Lone Islands stays well in tact, even though he hasn't been there for years.
As suggested by his title, Edmund is a just king. Debatably, it is Edmund's need for personal justice that makes him rebel so zealously against Peter and his sisters in LWW. Edmund thinks he has every right to be treated well, and when Peter does not treat him well, Ed starts thinking of ways to get revenge on Peter.
This is his sense of “justice” before it is turned into a good sense. When the White Witch demands his life, Edmund can think of nothing to say, probably because he knows the truth of what the Witch is saying. Aslan is the one who makes a stand for the dumbstruck Edmund, giving him a new idea of justice.
When Trumpkin and the Pevensies are fighting about which way to go in Prince Caspian, Edmund suggests a fair vote. He also ends up taking a stand for Lucy, which he believes is the fair thing.
During Eustace's dragon adventures in Voyage of the Dawn Treader, Edmund considerately tries to be patient with Eustace. He is also very stern and serious in telling Caspian not to abdicate the throne. Such a betrayal to Narnian people would be especially unjust.
Overall, Edmund is a bright, straight-thinking, and sarcastically witty king. One of his weaknesses was the wish to be famous, but after his encounter with the White Witch he mostly overcame this and proved himself to have a wise and loving heart. It seems after the encounter with the ghost of the White Witch, he is shaken up enough to be scared of her when the green mist tricks him that her ghost is hunting him.
In the movies, Edmund has a darker personality than in the books, as he remains a witty and quite brooding character. He is mostly silent and he is seen to have a frown on his face quite a lot. In Voyage Of The Dawn Treader, he is tempted again by the magic pond that turns everything into gold and he goes to the point where he tries to get rid of Caspian because Caspian opposes his plan of becoming powerful and rich along with Lucy. He is also often tempted to use violence on his bratty cousin, Eustace, but he is mostly stopped by Lucy.
It is confirmed that C.S. Lewis intentionally compared Edmund to Judas Iscariot, the Biblical betrayer, because Edmund betrayed Aslan, who represents God/Jesus, and his siblings who are analogues for different Apostles, to the White Witch (the devil) for Turkish Delight, which is the silver that Judas betrayed Jesus for.
All these traits make Edmund the somewhat darkest one of all the Pevensie children before his first trip into Narnia.