[wosk]

yes exactly, it's a conditional forecast. I intended: P(Rain tomorrow | my model is right) = 0.7 p(my model is right) = .8 p(my model is wrong) = .2 p(rain tomorrow | my model is wrong) = something_you_believe_about (= 0.1 in my example) 0.80.7 + 0.2 0.1 = 0.58

you may replace "my model is wrong" by e.g " my certainty that no one is using cloud-activation technology".

Now, I'm not native in English and I see how someone (especially with a math background) might find this sentence confusing:

> you are predicting something (e.g rain tomorrow), then if you believe it will rain with probability 0.7 but you are 80% sure of your belief, you won’t say 0.7; you will say something else: 0.8 × 0.7 + 0.2 × something_you_believe = 0.58. Coherence forces you to collapse your uncertainty into your probability at each forecast.

Turns out it's very hard about math non-formally for generalist audience and might not have done the best job about it. It should read

> you are predicting something (e.g rain tomorrow), then your model believe it will rain with probability 0.7 but you are 80% sure of your model, then you won’t report 0.7; you will report : 0.8 × 0.7 + 0.2 × something_you_believe = 0.58. Coherence forces you to collapse your uncertainty into your probability at each forecast.