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, I know I never turn up to work on time, have a horrible record for absence, don't put in any effort when I am here and constantly bicker with the other staff, but I have three kids at home. Surely you wouldn't let them go hungry by firing me?"
One common subtype is Think of the Children, in which the subject of the argument is claimed to adversely affect children. This works not only because it appeals to people's natural instinct to protect children, but because it implies that anyone who disagrees is a big meaniewho hates children.
The ubiquity of the Internet gives children greater access to pornography than at any point in history. We must do something to protect them from these vile images!
Another trope which can rely on this principle is Even Evil Has Loved Ones - the viewer may find themselves thinking "well, sure it's a shame that that little girl has lost her granddad, but then he 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..."
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. 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.