I didn't say anything of the sort.
> The reality is that likely they are acting based on very different premises from your own, extracted from their own life experiences and those of their ancestors.
That is true. That doesn't imply however that their beliefs draw solid statistical conclusion from those experiences.
For example, take rituals like rainmaking that are intended to change the weather. These were performed over many years and generations, and yet (we presume) never brought about any actual statistical improvement over not performing them. Those people would have experienced that (lack of) improvement directly. And yet they continued to believe it.
That's a great example given it is long-term, repetitive, and even non-experts should understand it. I'm going to try to remember it.
The occasional spectacular random success is far more memorable than a string of failures, because the string of failures simply proves the ritual wasn't done correctly. Or there's some other unknown reason why it didn't work.
It's also known that rewarding a behaviour at random is better at reinforcing it than constant reward - perhaps because the reward stimulus is fresh each time it's re-experienced.
https://www.schneier.com/blog/archives/2006/11/perceived_ris...
The one-off event of rain forming becomes the story that everyone remembers most and is passed down with dogma. It gets lots of momentum. Day-by-day data generated for years and analytically processed isn't quite memorable. This is same reason people are more afraid of airplanes despite cars killing more. More relevant, it's the same kinds of bias that makes people think they'll win it big in the lottery despite all evidence to the contrary. I've walked in on 50yd lines when PowerBall is up. They'll always say "But such and such up North won $100mil. You never know. It can't hurt to try."
Illogical as hell given that time and money could produce real benefit with high certainty. Yet, they continue doing it to try to re-create that one-off moment someone else experienced. And then someone else experienced it again. :)
So we comply with the ritualistic behavior in a sort of group angst, when we win we feel it worked and when we loose we feel some sort of existential support system.
Also you're assuming that everyone has accurate evidence about the impact of weather rituals. In a society without written records, how is that supposed to magically happen?
Saying "maybe there's an explanation" for every case does not advance the discussion. Saying "maybe there's an explanation" for every datum that does not fit your prior assumptions pretty much rules out statistical thinking, even if you otherwise have the capability.
So someone with bad priors can come to bad conclusions through entirely "rational" means.
Statistics and rationality merely work by measuring current events against your previous experiences and inferring the most probable outcome of your possible actions. That means that your previous life experiences and how you have interpreted and classified them are key in what your brain is going to expect from future events and in consequence how you are going to react to them.
In your example you are assuming these people are acting "irrationally" because they aren't taking the "correct" decision by your own judgment. The reality is that likely they are acting based on very different premises from your own, extracted from their own life experiences and those of their ancestors. Given the outcome, they were clearly wrong on their conclusions, but that only means that rationality and statistics are useless if you are basing your reasonings on wrong premises and there is no mechanism to stop you from feeding them the wrong data, not that these seemly absurd actions didn't have a somewhat rational justification.
About cognitive biases, well, your brain makes decisions based on the data it has available, and whenever it is insufficient it can't simply delay decision making until its confidence level is acceptable, hence it needs some heuristics to guarantee it gets a result whenever enough previous experience is lacking.