Broken compass argument
In philosophy or debate, a broken compass argument is a specific type of fallacious claim or assertion that starts with one premise and leads equally to many disparate (often mutually incompatible) conclusions.
If a person were to argue that they know that the Christian God exists because when they pray they feel better, they have made a broken compass argument because any other praying member of any other faith could make the same claim for their deity's existence following the same argument; e.g. Allah is real because a Muslim feels better when they pray, Vishnu is real because a Hindu feels better when they pray, etc.
Based on Moroni 10:4:
However, many religions make this claim and also have spiritual experiences. Therefore, no particular God is demonstrated by this method.
Derivation of the Name
The name derives from the fact that while a working magnetic compass will self correct if turned, a broken compass will not, entailing that a broken compass can be turned in any direction. The broken compass argument likewise "points in multiple directions" and thus can't be used to find one's way (to truth) any more than a broken compass can be used to find one's cardinal direction.
The broken compass argument is a sub class of the non sequitur fallacy used to illustrate the precise fallaciousness of trying to prove one conclusion where many exist logically. Arguments from faith, ignorance, consensus, tradition, authority, or emotion are all broken compass arguments by their very natures. Arguments from reason self-correct like a working compass, unlike any of the preceding.