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There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck (ie receiving useful things in the game). 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, 2021 at 5:31
  • But that really isn't logically rigorous is it?
    – Some Guy
    Jan 13, 2021 at 22:43
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    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, 2021 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, 2021 at 23:15
  • @Conifold - Don't even look in to how many times people are falsely convicted, let alone the larger amount that a pretty surely guilty person is acquitted. Judgement is an imperfect system, certainly.
    – Scott Rowe
    Jun 7, 2022 at 9:41

2 Answers 2

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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, 2021 at 3:56
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    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, 2021 at 4:21
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    Why should we think that "10 millions users tried 100 times"?
    – Dave
    Jan 20, 2021 at 22:34
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    @Dave: it's just a ballpark estimation that seems reasonable. 10 millions people attempting speed runs worldwide for 126 million actual users (according to google) and 100 tries, considering speed runs that dont go well from the start will be abandoned quickly, looked reasonable to me. I wouldn't bet my breakfast on it though.
    – armand
    Jan 20, 2021 at 23:09
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    Now that the guy actualy admited he cheated, that answer feels odd. But the logic is still valid.
    – armand
    Oct 10, 2021 at 9:30
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No, this is not a good example of the fallacy.

The argument from personal incredulity fallacy is called like that when the a subjective likelihood is exaggerated or its interpretation is exaggerated, and a flawed alternative otherwise impossible is pushed.

Such as suggesting evolution must be false, and God must have created humans, because it is unlikely that genes randomly take the necessary shape.

In this case, the likelihood is not exaggerated but objectively calculable, and the suggested alternative is easily possible.

If cheating in games was much harder as an alternative, the judgement of the most likely explanation might be different.

Note that just because this argument is not tainted by that fallacy, it is not proof that a cheat happened, but just sufficient evidence to make minor decisions. In life, it's common to have to choose between two possible alternatives that can both be easily true but one being more likely than the other. There is no clear line to be drawn when the less likely one needs to be discarded.

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