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Attempting to make someone feel sorry for either the arguer or the subject of the argument, in order to convince them to accept the argument regardless of its validity.
Sir, you shouldn't fire me, even though I'm chronically late, bicker with all the other staff, and consistently fail to finish my tasks on time, because I have a sick wife and four children and if I lose my job we'll be thrown out of our house and have to live on the street."
Even Evil Has Loved Ones and Pet the Dog - the viewer may find themselves thinking "Well, yes, that guy did hole himself up in a fortified chapel with fifty hostages so he could open a portal to hell with the unholy power of their tormented souls. But killing him means that sweet little girl will lose her grandfather who she loves dearly."
Researchers have shown that the best predictor of the outcome of a malpractice lawsuit in the United States is not whether there is evidence that the physician actually erred, but the status of the patient and the severity of the result. For example, (in the US) if a newborn has a malformation, the odds of an award are distressingly high, even when there is no evidence that the cause is anything except bad luck. Obstetricians have absurdly high malpractice insurance as a result, and that cost is picked up ultimately by the patients.