alt Hacker Newshttps://link.springer.com/article/10.3758/s13423-015-0947-8#...
https://sami.boo/jaynes/confidence-intervals-vs-bayesian-int... (+ Cauchy example below)
It’s like with test accuracy. Test accuracy is the pre-test probability that the test will give a correct result. But once you have a positive or negative result, which way it turned out plays a part in computing the predictive value. Likewise, once you have computed the interval, the specific bounds you ended up getting can affect the plausibility that they contain the true value.
Your first link is just the pedantry. The second link... I don't see any issue for the question I asked? The confidence interval is supposed to be wrong a certain percent of the time. It being so wrong it disproves itself is funny but the 90% is still 90% isn't it? They just landed in a particularly harsh part of the 10%.
The conclusion they come to is "it is possible to do better in the individual case by taking into account evidence from the sample that the confidence interval method throws away". That means the confidence interval is inefficient, not incorrect.