Appeal to Audacity

What I'm worried we're in danger of doing here is, having heard something that is absurd and obviously not true, and saying that therefore it must be true...

—David Mitchell, Would I Lie to You?

Or, what happens when a Genre Savvy character realizes that the incredibly absurd story he's just been told has to be true — for the simple reason that no one in his right mind would claim such a ridiculous story unless it were true.

After all, think about it. What happens to someone in movieland who claims that aliens are taking over people's bodies and passing themselves off as the originals to act as a prelude to an alien invasion? Loony. And then, of course, the aliens come and kill us all. So considering the risk and reward of making an outrageous claim, why would anyone in his right mind say such a thing unless he had good reason to believe it? This doesn't even get into the fact that if someone is trying to manipulate you with lies, it is obviously in their best interest to come up with more plausible ones.

When somebody creates an audacious lie and expects people to believe it because no one in his right mind would claim such a ridiculous story unless it were true, the lie is a Big Lie (and an intentional playing with this trope).

Contrast Cassandra Truth, in which authority figures refuse to believe an implausible tale.

Examples of Appeal to Audacity include:

Anime and Manga

In Death Note when Mello tells Near about the killing notebook and the shinigami, the SPK asks Near if he could really believe such a story and he says that if Mello were lying to them he wouldn't tell such a ridiculous story so it must be true.

Comic Book

In Watchmen, Rorschach's reaction to Moloch's story about the Comedian breaking into his room to sob about Ozymandias' plan is, "Sounds unbelievable. Probably true."

Film

A rather innocuous example in Ghostbusters:

Egon: She's telling the truth; at least she thinks she is.
Dana: Well, of course I'm telling the truth! Well, who would make up a story like that?

- She is telling the truth, of course, and they do take her story seriously (well, except for Venkman, who just pretends to so as to get in her pants).
Played with in Penn & Teller's movie Invisible Thread. Aliens plan to destroy the human race because there is nothing unique about us. Penn demonstrates Earth's uniqueness by claiming we've invented invisible thread, and goes on to perform a simple magic trick. The aliens decide immediately to leave the world alone. The kicker is that they privately inform Penn that humanity's uniqueness wasn't the trick, but rather our capacity for utterly ludicrous lies.
A memorable scene in Charade involves the male and female leads claiming to a police officer they had not committed a murder the previous night, but each only offering the alibi that they had been in bed, alone, in their own hotel room. The officer quipped: "Clearly you must be telling the truth-" significant glance at the obviously-falling-in-love couple - "for why would you invent such a ridiculous story?"

Literature

In the Sherlock Holmes story "The Boscombe Valley Mystery", this is what leads Holmes to believe that the young man who has been arrested may be innocent after all—the statement he gave the police is too stupid to be a lie.
In the first book of The Wheel of Time, Queen Morgase chooses to believe Rand's story because it is simply too absurd to be a lie. She notes at the same time that a clever liar would take advantage of this trope, but decides not to act on that impression.
In Tamora Pierce's Tortall Universe, Ally (of the Trickster duology) explains to her friends that she wasn't there to stop Sarai from eloping because she was being held captive by a god. She points out that, since she's a spymaster, "You forget I like to tell lies that will be believed."
In The Lion, the Witch and the Wardrobe, Professor Kirke uses this as the reason for why he believes Lucy's story about the wardrobe - if she had been lying she would have hidden for long enough that people started looking. (There's also the fact that he's been there himself, but CS Lewis hadn't thought that part up yet).
Arthur C. Clarke's "Tales From The White Hart" series of short stories concerns a "scientist", Harry Purvis, that tells scientific tall tales at a London pub called the White Hart. His outrageous stories' scientific logic is often called into question, but he is kept around for entertainment's sake. The exception is one story, "What Goes Up", totally made up to deal with an annoying conspiracy theorist. The end reveals Harry's obvious bullshit is taken totally seriously by the conspiracy theorist, and poor Harry gets bombarded with mail by other nutjobs-turned-fans. In other words, the one story he never wanted anyone to believe was the only one people actually believed.
In A Song of Ice and Fire, this is how Brienne manages to convince several people that she was not the one who killed King Renly despite being one of the only people in the room with him when he died. If she were the culprit, wouldn't she come up with a better story than "evil demonic shadow did it?"

Live-Action TV

When an anomaly causes all parts of the ship in Star Trek: Voyager to shift into random time periods in the ship's history, Chakotay finally comes up with a solution. Unfortunately, putting the solution into action requires a deck currently under control by Seska, Chakotay's old Love Interest turned villain. He reasons that the only way he can get her to cooperate is by being honest with her. While her subordinates are incredulous at the story, Seska declares it too implausible to be a lie.
This has happened in Stargate SG-1 a number of times. For instance, see the General Hammond reference in Seen It All. This may not count, though, because the characters have experienced other weird things, which gives them a reason to accept new ones—they don't just accept weird stories because they're too crazy to make up.
Subverted in the TV quiz show Talkin' 'Bout Your Generation, host Shaun Micallef will often make a long, detailed, and ridiculous statement and then ask if it is true or false. The contestants often assume that such a statement must, by virtue of this trope, be true, only to have Micallef then tell them that they are wrong and he made the whole thing up.
Similarly done on Spicks and Specks in "One Out of Three Ain't Bad". Adam tells a story with one true ending and two false endings. Played with when there are two equally far out endings, available and subverted when the team chooses the less implausible one.
An episode of Jonathan Creek has Jonathan defending the accused in this episode mostly due to this trope. The man is accused of kidnapping a young girl who was seen entering his house by several witnesses. His defence is that he was in that room staring at the door the entire day (after being robbed and tied up in the room) and didn't see anyone come in. Jonathan points out that this is such an incredibly stupid defence that he can't possibly be making it up. Of course, he's right. The truth is that after being knocked out during the robbery, he was taken to a nearby farm where a cult had recreated the interior of his room so he thought he was in it all day (later knocking him out and taking him back as he slept) so they could kidnap the girl and pin it on him, all in an attempt to get rid of the man's wife who had been critical of (and then stopped) his funding of the group.
- It's used again in the episode "Black Canary" when a man comes up with a seemingly impossible story about seeing his wife argue with an unknown man outside in the garden seconds before she shot herself - only for the man to leave no footprints in the snow. The police inspector on the case points out that the man is practically above suspicion - as why would he make up a story so impossible that no one would believe it?
In The IT Crowd, Roy's girlfriend tells him a ridiculous, incomprehensible story about the death of her parents. When Jen asks if she could have been lying, Roy answers, "Why would she lie? And if she was going to lie, why would she use this one? A fire at a Sea Parks?! It's wrecking my head! I mean if... if she had said that her parents had drowned, I'd be the happiest man in the world!"

Western Animation

One episode of King of the Hill involves Hank getting sent to a discretionary board on the charges of fraudulently claiming worker's compensation. Hank is unable to disprove the government's claims until he brings in the yoga expert who cured him to help verify the timeline of when he got injured and when he got cured. The board is initially very unimpressed with the yoga expert—but accept his story when Hank points out that the yoga expert is so obnoxious that Hank would have to have been suffering from a devastating injury indeed to be desperate enough to seek help from him.
A version of this appeared on The Simpsons. When the town thought that Skinner and Ms. Krabappel were having sexual relations at school, Skinner cleared his name by telling them he was a virgin. This worked because, according to Superintendent Chalmers, no man anywhere would ever pretend to be a 45-year-old virgin.

Real Life

Christianity, according to the early Christian writer Tertullian, whose "credo quia absurdum est" is possibly the earliest example of this trope.
- Unfortunately, this can be used for other religions, including the Church of Happyology. At any rate, religions are originally very simple stories ("there is a God") that have had thousands of years to flesh out.
- It is perhaps worth noting that the official Church, with its strongly rationalistic bent, never cared much for this argument; Tertullian himself was regarded as a schismatic, if not an outright heretic.
- On a related note, Biblical scholars have something called the "criterion of embarrassment", which they use (along with other methods) to sort out which events of the New Testament are actual history. The criterion of embarrassment is basically "If it doesn't make Jesus look good (in a first-century context), then it probably really happened." This is why the crucifixion is well established as actual history; crucifixion was about the most disgraceful death that you could have in ancient Rome, and was reserved for slaves, pirates, and traitors. If the writers of the Gospels had wanted to make up a good death story for Jesus, it would have been very, very different.
  - The mainstream Christian account is that Jesus martyred himself for the good of the entire human race. I'd say that makes him look pretty good in any context.
  - Yes, but that's just a positive spin on a bad death. If they wanted, they could have had him burst into flames, fly into the stratosphere, explode, and make it rain acid on a legion of Roman soldiers for your sins.
  - The Apostles don't come off looking very good on the night Jesus was arrested.
  - In the context of the Old Testament, a people that was fabricating a history for itself probably wouldn't include the fact that they used to be slaves.
This trope is also the theory behind the propaganda technique known as the Big Lie. According to Hitler and Goebbels, if you are going to lie, don't say something that sounds like it might be true. Say something so outrageous that people will think that it must be true, because no one would make up a story like that.