Imagine that before a test, the professor told Jake that if he is caught cheating, he will be expelled. Imagine that the professor told Amanda that, if caught cheating, her only punishment will be to write a short paper about why cheating is wrong. If both students don't cheat, what would dissonance theory predict

Cognitive dissonance theory says that individuals feel discomfort when their attitude and their behaviors are dissonant, that is, in conflict. If you believe you should be good to others but lose your temper and snap at people easily, you will feel such discomfort. To stop feeling it, you will either change your belief/perception of yourself or your behavior.

In the situation described in the passage, Jake and Amanda were threatened with very different kinds of punishment, Jake's being much more serious. Thus, if he does not cheat, it will feel as if it was just because he was afraid to be expelled. Now, if Amanda doesn't cheat, it will feel as if she made that choice on her own, not because she was afraid of some dire consequence. She will feel better, more honest, about herself than Jake will.