Thanks for the response!
I don’t think there is any difference in those lists! Here’s why:
The impressiveness of 50% predictions can only be evaluated with respect to common wisdom. If everyone thinks P is only 10% likely, and you give it 50%, and P turns out to be true, this is impressive because you gave it a surprisingly high percentage! But also if everyone says P is 90% likely, and P turns out to be false, this is also impressive because you gave it a surprisingly low percentage!
I think what you’re suggesting is that people should always phrase their prediction in a way that, if P comes true, makes their prediction impressive because the percentage was surprisingly high, i.e.:
Most people think there is only a 20% chance that the price of a barrel of oil at the end of 2020 will be between $50.95 and $51.02. I think it’s 50% (surprisingly high), so you should be impressed if it turns out to be true.
But you could also say:
Most people think there is an 80% chance that the price of a barrel of oil at the end of 2020 will not be between $50.95 and $51.02. I think it’s only 50% (surprisingly low), so you should be impressed if it turns out to be false.
These are equally impressive (though I admit the second is phrased in a less intuitive way) - when it comes to 50% predictions, it doesn’t matter whether you evaluate it with respect to ‘it turned out to be true’ vs ‘it turned out to be false’; you’re trying to correctly represent both the percentages in both cases (i.e. the correct ratio), and the impressiveness comes from the extent to which your percentages on both sides differ from the baseline.
I think what I’m saying is that it doesn’t matter how the author phases it, when evaluating 50% predictions we should notice both when it seems surprisingly high and turns out to be true, and when it’s surprisingly low and turns out to be false, as they are both impressive.
When it comes to a list of 50% predictions, it’s impossible to evaluate the impressiveness only by looking at how many came true, since it’s arbitrary which way they are phrased, and you could equally evaluate the impressiveness by how many turned out to be false. So you have to compare each one to the baseline ratio.
Probability is weird and unintuitive and I’m not sure if I’ve explained myself very well...
Thanks I appreciate that :) And I apologize if my comment about probability being weird came across as patronizing, it was meant to be a reflection on the difficulty I was having putting my model into words, not a comment on your understanding