Skyrim Sidelines- Mind of Madness: It is Not I Who am Mad, It is I Who am Crazy

The clearing to the Southeast is centered around Pelagius' hatred and anger.  As it turns out, there is very little the man hates as much as he hates himself- this is both explained by Sheogorath and apparent by the two occupants of the clearing- a pair of copies of Pelagius the Mad, labeled 'Anger' and 'Self Confidence'.  Since you cannot talk to them and Anger is incessantly beating up Self-Confidence, you'll have to do as Sheogorath suggested and find a way to even the match.

Being as all you have on hand is Wabbajack, you'll have to use that.  Use the staff to throw a blast at Anger, and he will shrink- keep this up until he stops shrinking.  Then turn your attention to Self Confidence.  This time, the staff promotes growth- but Anger has a bit up his sleeve and will pull out a pair of axes when Self Confidence matches his size.  Zap Confidence again to make him the larger of the two and complete the clearing.  Sheogorath will compliment you on altering Pelagius' mind so that he no longer hates himself as much as he hates everything else.  According to the mad Daedra, this is an improvement.... probably.

The Northwest clearing contains a stadium, where two elemental atronach battle.  You are opposite another incarnation of Pelagius, protected by a pair of guards, and the atronach are unreachable to you.  Sheogorath informs you that Pelagius is constantly fighting himself, leaving him wracked with indecision.  To solve this, he says you must use the Wabbajack on your opponent.

You can use the Wabbajack on one of the atronach in the arena- but each time you do, the other atronach changes within a couple of seconds, regaining the elemental advantage.  You can keep this up as long as you like to no effect.  The trick, of course, is to use the Wabbajack on your opponent- and not your opponent's tool.

Blasting Pelagius will cause him to vanish, and blasting his guard (either one) will turn them both into wolves which then attack the mad king.  Thus, with his paranoia no longer prompting him to argue with himself (and instead prompting him to argue with everyone else), you have completed this task and earned praise from Sheogorath.