1/ I've noticed that a lot of people who pride themselves on being "rigorous" or "critical thinkers" have this simple heuristic that anecdotes = weak evidence.

But I disagree! It depends on what claim those anecdotes are being used to support.
2/ For example, in one chapter of my book I tell a few anecdotes of successful leaders who express uncertainty (e.g. Jeff Bezos saying "Amazon has a 30% chance of success")
3/ Some readers scoffed at this "anecdotal evidence." But I think they assumed I was using those anecdotes to support a claim like (a) "Expressing uncertainty will make you a successful leader."

And yes, I agree that a few anecdotes WOULD constitute weak evidence for that claim
4/ But that's not the claim I was making. Instead, I was claiming (b) "It is possible to be a successful leader and express uncertainty (contra the common wisdom, which says it isn't)."

That's a weaker claim and one which actually only needs a handful of anecdotes to justify it
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