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This is not a fallacy, just the old problem of induction. A case of hasty generalisation would be to conclude that the witness tends to lie, if you have observed it two times in a row.

All informal fallacies take their force from their similarity to strong arguments. In this case, if you say "This boy lied 19 days in a row, therefore we have good reason to disbelieve him on Day 20," that is a perfectly good argument (assuming it isn't suppressing other relevant information).

But if you say "This boy lied 19 days in a row, therefore what he told us on Day 20 must be a lie" then you are overreaching the evidence. The evidence suggests the boy may be lying, it does not entail it, prove it, or establish it. If there is independent support for the Day 20 statement, yet you insist on it being a lie because you heard it from the boy, you are committing the genetic fallacy, also known as the fallacy of origins.

Genetic Fallacy: A genetic fallacy is a logical fallacy that occurs when a claim is accepted or rejected based on the source of the evidence, rather than on the quality or applicability of the evidence. It is also a line of reasoning in which a perceived defect in the origin of a claim or thing is taken to be evidence that discredits the claim or thing itself. The fallacy is committed when an idea is either accepted or rejected because of its source, rather than its merit.
https://rationalwiki.org/wiki/Genetic_fallacy

I think I found something that comes close:

Appeal to probability (Wikipedia)

An appeal to probability (or appeal to possibility) is the logical fallacy of taking something for granted because it would probably be
the case (or might possibly be the case).

and

An appeal to probability argues that, because something probably will
happen, it is certain to happen.

The fallacy is an informal fallacy.

P1: X is probable.

P2: (Unstated) Anything which is probable, is certain.

C: X is certain.

The fallaciousness of this line of logic should be apparent from the second, unstated premise (P2), which seems and is blatantly false.

Appeal to Probability - Rational Wiki

I was thinking along the lines of appeal to history or something, not sure if such a term exists. I'd still appreciate any more suggestions.

In your analysis, there must be some intellectual problem with "disbelieving someone on Day 20 because they have lied every day previous to Day 20." I could split this into these parts:

1) Donald lied to me each day for 19 days straight up to yesterday.

2) Donald said something to me today, and wants me to believe it in spite of the past 19 days of lies (which he acknowledges).

3) The thing Donald said to me is false because all the other things Donald said were false.

Clearly, 3) is an incorrect conclusion: the thing Donald told me today is either true or false quite independently of the history for the past 19 days. In fact, Donald's intention to deceive me could have switched and he may intend to tell the truth to me today, while he intended to lie before. In addition, Donald may well be mistaken: he may be wrong about whatever it is today, thus rendering the truth/falsity of his words today in opposition to his intention today to deceive or to tell the truth.

But let's suppose that someone has thought this instead:

1) Donald lied to me each day for 19 days straight up to yesterday.

2') Donald said something to me today, and wants me to take some action upon it in spite of the 19 days of lies (which he acknowledges).

3') I don't feel safe taking any action upon Donald's words today unless another independent person tells me something about the issue, positive or negative.

Corollary to 3'): I am willing to investigate the thing Donald was telling me today, because it shouldn't be too hard to figure out independently if it's true or not.

There is no fallacy with this reasoning, since it is completely reasonable to take action or not, and to assume the risks of action or inaction, based on your best guess of the trustworthiness of Donald's words. On the chance that "there really is a wolf this time", you can protect yourself by spending the extra effort to validate Donald's claim.

If I already spent the effort to investigate Donald's claims on days 1 through 19 and found them to be false, then the action Donald wants me to take today amounts to "see for yourself", and I don't even have to do that. In old-fashioned legal terms the appropriate action is to "censure" Donald, meaning that as far as I'm concerned, his words no longer cause anything.

This isn’t an exact fit, but the logic here is similar to the Hot Hand Fallacy. Because something has occurred frequently in the past, it in some way informs likely future events, with the assumption events will continue to transpire in the same way.

It’s not a perfect fit, as the Hot Hand Fallacy specifically concerns streaks of successes making people believe success (specifically) is more likely.

Some times also called the Hot Streak Fallacy.

This isn't quite a fallacy, but what you're talking about is likely caused by Apophenia. From the Wikipedia page:

Apophenia (/æpoʊˈfiːniə/) is the tendency to mistakenly perceive connections and meaning between unrelated things. [...]

Apophenia has come to imply a universal human tendency to seek patterns in random information, such as gambling. [...]

In statistics, apophenia is an example of a Type I error – the identification of false patterns in data. It may be compared with a so-called false positive in other test situations.

In more casual terms, its the human ability to seek out patterns where there may or may not be any. If a man lies to you three days in a row, you may see a pattern and not trust him on the fourth day when he cries wolf again. This is apohpenia at work.

Consider the 'Availability Heuristic',

Under the availability heuristic, people tend to heavily weigh their judgments toward more recent information, making new opinions biased toward that latest news.

More broadly, it could be considered confirmation bias

We are primed to see and agree with ideas that fit our preconceptions

You may be looking for the Illusory truth effect.

The illusory truth effect (also known as the validity effect, truth effect or the reiteration effect) is the tendency to believe information to be correct after repeated exposure

According to Fazio L. et al:

Repetition makes statements easier to process, relative to new statements, leading people to the (sometimes) false conclusion that they are more truthful.

This sounds like Gambler's fallacy, a "reverse" version of it: https://en.wikipedia.org/wiki/Gambler%27s_fallacy#Reverse_position

Namely, believing that the coin is more likely to land on one side if there was already a tendency towards that side in the past.

I'll give it a try with probabilities. Most of them guessed out of the blue, so please feel free to correct me if you have data.

I'll tackle the 10 lies out of 13 answers scenario.

• I'll assume for now that we know for sure that these 10 are lies (which sounds not that plausible to me - I don't think it's so easy to actually prove a lie and considering that, this sounds extraordinarily patient... But what I'm going to do will mostly hold also with honest mistakes on the side of the witness).




• I'll assume a mistakenly false witness statement to happen in roughly 1 % of answers.
  
  This number is somewhat arbitrarily pulled from the range of innocent suspects wrongly identified by eyewitnesses in Mickes, Flowe, Wixted: Receiver Operating Characteristic Analysis of Eyewitness Memory:
  Comparing the Diagnostic Accuracy of Simultaneous Versus
  Sequential Lineup, Journal of Experimental Psychology: Applied, 361 – 376, 2012 and the corresponding probability to correctly identify the guilty party around 1 in 5 times.




• We'll also assume that all those answers and questions are independent of each other, and



• that the witness behaviour can be summarized by a single "probability to lie"

This is obviously a vast oversimplification of what happens in real life. However, I think the scenario is still useful to show how much evidence we have and how much we do not have.

To be continued, have to leave for today