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There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck. A moderator team has calculated that the p-value of the chance you'd get the same drops as Dream just by chance is in the magnitude of 10^-12. So, the moderator team concluded that Dream was cheating, and so did many others. However, isn't this an argument from personal incredulity? There's a nonzero probability that Dream just got lucky and wasn't cheating, even if the probability is very small. This means that people think Dream is cheating just because they can't believe he got that lucky, so isn't that a personal incredulity argument? I also think that it is obvious that Dream is cheating, but I do not know whether this proof is rigorous or not.

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    No, it is not. Incredulity is a psychological reaction: I can not imagine how it could happen, therefore it didn't. Calculating probabilities and showing that something is unlikely, whether such statistical analysis is flawed or not, isn't incredulity. Genetic matches work on the same principle, they are statistical analyses that give estimates on probability of parentage, and decisions are made based on them. In fact, since all real life information has some degree of uncertainty if we were to adopt "Dream just got lucky" principle we won't be able to draw any conclusions at all. – Conifold Jan 13 at 5:31
  • But that really isn't logically rigorous is it? – Some Guy Jan 13 at 22:43
  • If I have a grain of sand, it's a grain of sand. I add another grain, and its still some grains of sand. At what point does it become a heap of sand? It is subjective opinion. Likewise, how do you decide what is TOO lucky objectively? – Some Guy Jan 13 at 22:44
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    Predicates like the heap are called vague. The way to deal with them is not subjectivity but convention, decision calls are made when the conventional threshold is reached. For example, scientists agree on the standards for measurement reliability (5 sigma standard), courts agree on the standards for genetic and fingerprint matches admissible as evidence, etc. Just because a threshold is conventional does not mean it is subjective. Real world isn't mathematics, empirical judgments can never be "logically rigorous", so that "standard" is moot. – Conifold Jan 13 at 23:15
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Hey there fellow Minecraft lover.

If one is to be rigorous, it is a fallacy by personal incredulity: there is after all a 1 in 1000 billions chance that he did not cheat, so you can't rule out the possibility. One rational way to approach it is to consider how many speed runs of minecraft have been attempted in the whole world so far. If we take a conservative estimate of a billion attemps (10 millions users tried 100 times), the probability of this configuration of drops never happening is (1-10^-12)^(10^9)=0.999, so one chance in a thouthands that it would happen one day. Pretty small but orders of magnitude less improbable. I would require some evidence of the cheating before having a definitive judgement. Part of the decision about cheating is in my opinion due to the mind boggling number of 1/10^-12. If we consider the probability more carefully the number becomes 1/1000 and suddenly it's a lot less clear cut, showing that for the same facts the presentation of the case played a big role in eliciting an emotional response rather than a rational one, exposing the fallacy.

Now, the important thing to take away from this is you don't have to decide now for yourself if he cheated or not. Just be highly doubtful that he managed his performance fairly, along with the recognition of the fact that he was clearly incredibly lucky, which makes the performance less impressive.

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    Your rational way is just another probability scenario – Some Guy Jan 13 at 3:56
  • You answered my question whether it was personal incredulity or not, so I will accept it. – Some Guy Jan 13 at 3:56
  • yeah, it would still be incredulity. I just wanted to show that part of the decision about cheating is in my opinion due to the mind boggling number of 1/10^-12. If we consider the probability more carefully the number becomes 1/1000 and suddenly it's a lot less clear cut, showing that the presentation of the case played a big role in eliciting an emotional response rather than a rational one, i.e. it's a fallacy. – armand Jan 13 at 4:21
  • Since you are new i would like to advise you that you don't have to accept my answer so fast even if it satisfies you. Give someone else the chance to produce a better one, so that people who might read your question in the future can enjoy the best of the best displayed at the top. – armand Jan 13 at 4:25
  • got it thank you – Some Guy Jan 13 at 4:52

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