What are the Ad Verecundiam, Petitio Principii, and "appeal to popularity" fallacies?

Three classic fallacies: bad appeal to authority, begging the question, and the bandwagon.

• Ad Verecundiam (appeal to authority) — citing an authority as if that settled it, when the authority is irrelevant, biased, or not a genuine expert on the point. (Appealing to a real, relevant expert is fine; the fallacy is the illegitimate appeal.)
• Petitio Principii (begging the question) — assuming the very thing you're trying to prove. The conclusion is smuggled into the premises, so the argument moves in a circle and proves nothing. ("The Bible is true because it's the word of God, and we know that because the Bible says so.")
• Appeal to popularity (bandwagon) — "lots of people believe it, so it's true." Numbers aren't evidence; a majority can be wrong. This family also includes appeals to emotion, tradition, novelty, pity, spite, belief, etc. — each substitutes a feeling or a crowd for an actual reason.

The common thread: a non-reason is dressed up as a reason — authority, circular restatement, or popularity standing in for evidence.

Tip: "Begging the question" in its strict logical sense means assuming what you set out to prove — not "raising a question." Catch it by checking whether a premise secretly is the conclusion.