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Subverted: Alice regularly makes claims that sound absurd. It turns out that this universe operates under different laws than they're used to.
Double Subverted: While the universe may operate under different rules, Alice's claims are still wrong.
Parodied: Alice is constantly wrong - but the rest of the world doesn't think so. In fact, she has a global reputation as a fountain of wisdom due to an overwhelming personality, a big bank account (which she uses to toot her own horn) and a very few lucky guesses. Anyone challenging her will be hooted and hawed at best.
Zig Zagged: Alice is an idiot when it comes to some subjects, but a genius when it comes to others; her self-confidence also wavers depending on the subject. She recognizes that her knowledge in some areas is woefully inaccurate, and underestimates her comprehension of other topics, but is also overconfident about topics she really doesn't understand that well.
Averted: Alice is fully aware of the limits of her own knowledge, and doesn't claim to be smarter than she really is.
Enforced: We want Alice to be annoying, and Insufferable Genius is not bad enough. Lets make her smart in her own head.
After hearing one of Alice's obviously absurd claims, Bob calls her crazy. Alice answers "Like a fox!"
"Alice Is just one of those self-proclamed smart idiots that don't know they are wrong".
Invoked: Alice is the First Lady to the President-For-Life of Tropesylvania, who gets very angry when someone makes her upset. People very quickly learned not to make Alice upset by agreeing to whatever nonsense she claimed to be true.
Defied: After Alice makes a particulary egregious claim, a REAL expert in the subject steps forward with the straight dope. They shoot down every logical fallacy and poisonous retort Alice spits out, and ultimately they drive her out of the room in tears.
Discussed: "Ever noticed how Alice speaks like a crazy person?"
Conversed: "And that is the character who is a idiot that thinks that knows more than everyone else".
Deconstructed: Alice's overestimation of her intellect comes back to bite her when she refuses to study for an important test on the information, assuming she'll breeze through it. She doesn't. In fact, she fails horribly and flunks the whole class, something which leaves her confidence severely shaken.
Reconstructed: It turns out the teacher was romantically involved with a student in the class; he's fired/arrested, the student is expelled and the rest of the class receives a passing grade. Alice assumes her poor performance was somehow due to the teacher's machinations and she regains her self-admiring style.
Played For Laughs: Alice is an arrogant, spoiled Alpha Bitch who thinks she is always right, only to be humiliated by the new transfer student who has a rudimentary understanding of the English language.
Played For Drama: Alice was criticized and belittled for most of her childhood and as a result developed this as a defense mechanism, however she can barely fuction in the society, having no friends and has a great deal of trouble in holding a job.