A typical situation is that there's a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.
You have three ways to respond:
In almost every situation you're likely to encounter, the real danger is 3. Well-known biases are at work pulling you towards 3. These biases are often known to work even when you're aware of them and trying to counteract them. Moreover, the harm from reaching 3 is typically far greater than the harm from reaching 1. This is because the correct added amount of credence in 2 is very tiny, particularly because you're already likely to know that the competing hypotheses for this issue are all likely to have anecdotes going for them. In real-life situations, you don't usually hear anecdotes supporting an incredibly unlikely-seeming hypothesis which you'd otherwise be inclined to think as capable of nurturing no anecdotes at all. So forgoing that tiny amount of credence is not nearly as bad as choosing 3 and updating, typically, by a large amount.
The saying "The plural of anecdotes is not data" exists to steer you away from 3. It works to counteract the very strong biases pulling you towards 3. Its danger, you are saying, is that it pulls you towards 1 rather than the correct 2. That may be pedantically correct, but is a very poor reason to criticize the saying. Even with its help, you're almost always very likely to over-update - all it's doing is lessening the blow.
Perhaps this as an example of "things Bayesianism has taught you" that are harming your epistemic rationality?
A similar thing I noticed is disdain towards "correlation does not imply causation" from enlightened Bayesians. It is counter-productive.
A typical situation is that there's a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.
It is interesting that you think of this as typical, or at least typical enough to be exclusionary of non-contentious issues. I avoid discussions about politics and possibly other contentious issues, and when I think of people providing anecdotes I usually think of them in support of neutral issues, like the efficacy of understudied nutritional supplements. If someone tells you, "I ate dinner at Joe's Crab Sh...
David Chapman criticizes "pop Bayesianism" as just common-sense rationality dressed up as intimidating math[1]:
What does Bayes's formula have to teach us about how to do epistemology, beyond obvious things like "never be absolutely certain; update your credences when you see new evidence"?
I list below some of the specific things that I learned from Bayesianism. Some of these are examples of mistakes I'd made that Bayesianism corrected. Others are things that I just hadn't thought about explicitly before encountering Bayesianism, but which now seem important to me.
I'm interested in hearing what other people here would put on their own lists of things Bayesianism taught them. (Different people would make different lists, depending on how they had already thought about epistemology when they first encountered "pop Bayesianism".)
I'm interested especially in those lessons that you think followed more-or-less directly from taking Bayesianism seriously as a normative epistemology (plus maybe the idea of making decisions based on expected utility). The LW memeplex contains many other valuable lessons (e.g., avoid the mind-projection fallacy, be mindful of inferential gaps, the MW interpretation of QM has a lot going for it, decision theory should take into account "logical causation", etc.). However, these seem further afield or more speculative than what I think of as "bare-bones Bayesianism".
So, without further ado, here are some things that Bayesianism taught me.
What items would you put on your list?
ETA: ChrisHallquist's post Bayesianism for Humans lists other "directly applicable corollaries to Bayesianism".
[1] See also Yvain's reaction to David Chapman's criticisms.
[2] ETA: My wording here is potentially misleading. See this comment thread.