Ok you have a story. I can tell a different story: "My tendency towards religious/supernatural belief that has helped me and my ancestors form moral codes and act tribally has in this case caused me to embrace a belief that will lead to the ruin of me and my people. These religious/supernatural beliefs are inherently anti-statistical and lead to lots of incorrect ideas like witchcraft and rainmaking, but these systems of belief are selected by evolution because they overall increase our chances of survival."
Now we have two stories, two narratives. Why do you believe yours over mine? And how can we objectively decide which story reflects the truth about the human brain?
No they aren't. They follow the Laplace–Bayes estimator for calculating the rule of succession[1].
I needed rain -> I did a rain dance -> it rained
I needed rain -> I did a rain dance -> it didn't rain -> I must have done something wrong
Both are perfectly valid rules of succession - not forgetting that most religious beliefs make it pretty easy to find something you did wrong. One might suspect these rules could have been caused by spurious statistical relationships.
This is a textbook example of a non-falsifiable experiment. I'm not sure why you would argue that you can draw meaningful statistical inferences from such an experiment.
"Statistically valid" != Correct (if your input assumptions are incorrect).
See up thread for ways to build falsifiable experiments.
If you mean "mathematically correct" then yes that is my premise.
If you mean "correct in reality" then no.
If you have a prior belief "god created humans" with a 99% confidence, it will take a lot of evidence to override that - especially since the evidence will be a long way down a causality chain (as any online argument about evolution will show). Additionally, the confidence in that belief will be erroneously increased by lots of things you see in nature (eg - humans cannot create other life forms, therefore it must have been done by something supernatural).
I'm not even saying the hypothesis is necessarily false. However I will never trust the results of people who become so attached to an idea that they focus entirely on confirming it rather than rigorously testing whether it actually reflects reality.
Different priors probably mean entirely different lines of reasoning, so you can't even say "well they should have thought about it the way I do" because it's not like the human brain is a single 10x10 neural net with no feedback, it's probably 1Mx1M and it is recurrent; the output from one time step feeds into the input at the next one.
You could get very, very different output for the same input from two neural nets that have been trained on different data. But that doesn't somehow make them not both neural nets; the meta-structure is the same even though all the weights from node to node are different.
Yes, exactly!
If you say "the machinery operates in way X" (where X="Bayesian statistics"), you have to actually prove that. You can't just assert it and say that people who disagree with you have bad priors.
I have no doubt that you can construct a hypothetical Bayesian decision-making process that could have yielded any possible decision that any human has ever made. Just like any religious person can take any story that has ever happened and construct a story about why it is compatible with the existence of God.
But unless you have a falsifiable experiment to prove that the brain actually operates this way, your explanation is an unverifiable just-so story. And in this case I don't find it at all convincing.
Don't get me wrong, I understand your theoretical argument. I just think you are taking an unjustified (in my perspective) leap of faith to presume that your story reflects reality.
I'm a bit frustrated that the original comment is the top voted comment, when it is at least more wrong than right.
But if this was a problem I was particularly motivated to study, the most satisfactory method of reaching a conclusion would be to use statistical analysis to draw conclusions about which hypotheses human thought patterns appeared to be most compatible with (from my experiments and meta-analysis of others'). I don't claim to know whether this is a refinement of my innate human tendency to be impressed by statistical support for a proposition or an unusual level of abstraction I've learned to reason at after spending too much time in an undergrad classroom.
But the actual point I was making in the message you replied to is much weaker than this. I was arguing that just because we can spin a narrative that says a decision-making process was based on a statistical process doesn't mean that our narrative is true. Just because you can tell a story doesn't mean the story reflects reality. We need some objective way of determining which of several competing narratives is actually true.
"This cattle-killing sounds crazy but since she was right about some other low probability events the probability of her being an actual prophet is pretty high, given the existence of prophets is not inherently improbable" and "my odds of survival are better if I follow this stupid recommendation than if I'm lynched by my fellow countrymen for ignoring it" are both statistically valid conclusions in favour of following some ridiculous food-source-decimating millenialist prophecy in certain circumstances.