Logical Fallacies as Weak Bayesian Evidence: Argument from Anecdote

06 Jun

Another juicy logical fallacy that gets repeated over and over on teh Internetz due to how thoughts are cached in your brain like webpages on your computer. Again, the problem is that people treat anecdotes as strong Bayesian evidence, or even as a Prosecutor’s fallacy-like conclusion, when in all likelihood they’re probably just very weak Bayesian evidence. But evidence is evidence nonetheless. Like pressing the gas on your car, you can either press it so that you increase by 50 mph or by 5 mph. But acceleration is acceleration whether strong or weak.

So the argument from anecdote. This is taking an event that happens to you personally and using it in an argument for a general explanation. Let’s take a situation that I obviously think is false, like ghost stories. Someone tries to convince me that ghost are real because they once heard a creaky floor in an old abandoned house and got a feeling of dread. Obviously, this isn’t conclusive evidence of the existence of ghosts. Butassuming that ghosts are real, this would “fit” into that worldview. And that’s the rub.

I personally think there’s a 1 in a trillion chance that ghosts are real. So I’ll use that number to demonstrate why an anecdote can still be used as evidence but not as a conclusion. Just like in my example of falsifiability using Bayes Theorem, let’s assume that I have a jar that has two types of dice: One that is a normal sided die with 1 – 6 labeled and another that has just a 5 on all sides. But in this instance, the jar is filled with 999,999,999,999 normal dice and only 1 (one!) trick die that has a 5 on all sides.

If I grab a die at random from the jar and roll a 5, Bayes Factor says I should divide the probability of rolling a 5 given that I’ve rolled the trick die by the probability of rolling a 5 given that I’ve rolled the normal die. Given that I’ve rolled the trick die, the probability of rolling a 5 is 100%. Given that I’ve rolled the normal die, the probability of rolling a 5 is 16.7%. This quotient is greater than 1 so that means that rolling a 5 is evidence for having rolled the trick die. But the prior probability of rolling the trick die in this case is basically a trillion to one, so in the end it is much more likely that I had grabbed a normal die.

Regardless, rolling a 5 is weak Bayesian evidence for having grabbed the trick die. Just like a ghost story anecdote is weak Bayesian evidence for the existence of ghosts.

Let’s try a more controversial anecdote, like “black people are stupid”. So someone grows up with this worldview of blacks having a low IQ while never having met a black person. The first time they meet a real live black person, the black guy they meet just happened to be in one of his high school classes and was the worst student. Assuming the hypothesis of stupid blacks is true, this anecdote fits that worldview. Maybe not at 100% like the trick die, but it’s a high probability. On the flip side, assuming this worldview is false there’s a much lower probability that this would happen. As a matter of fact, I would assume that exactly half of black people are below average intelligence, so the alternative hypothesis would say there’s a 50% chance that this would happen.

As it stands, the racist hypothesis puts more probability capital in seeing something like this than the non-racist hypothesis, so the racist hypothesis gets the evidence cash-out due to this anecdote. Just like with the trick die compared to the normal die. So again, in this case an anecdote can be legitimately used as Bayesian evidence. It might be strong or weak evidence, but it’s evidence.

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