Reading this, I was confused: it seemed to me that I should be equally willing to offer $2000 for each list. I realised I was likely enough mistaken that I shouldn’t actually make such an offer!
At first I guessed that the problem in lists like the second was cheating via correlations. That is, a more subtle version of:
The price of a barrel of oil at the end of 2020 will be between $50.95 and $51.02 (50%)
The price of a barrel of oil at the end of 2020 will be below $50.95 or above $51.02 (50%)
Then I went and actually finished reading the post (! oops). I see that you were thinking about cheating, but not quite of this kind. The slogan I would give is something like “cheating by trading accuracy for calibration”. That is, the rule is just supposed to remove the extra phrasing choice from a list to prevent shenanigans from patterned exploitation of this choice.
I now think a challenge to your post would complain that this doesn’t really eliminate the choice—that common wisdom is contradictory enough that I can tweak my phrasing to satisfy your rule and still appear calibrated at 50%-wards probabilities. To be clear, I’m not saying that’s true; the foregoing is just supposed to be a checksum on my understanding.
Reading this, I was confused: it seemed to me that I should be equally willing to offer $2000 for each list. I realised I was likely enough mistaken that I shouldn’t actually make such an offer!
At first I guessed that the problem in lists like the second was cheating via correlations. That is, a more subtle version of:
The price of a barrel of oil at the end of 2020 will be between $50.95 and $51.02 (50%)
The price of a barrel of oil at the end of 2020 will be below $50.95 or above $51.02 (50%)
Then I went and actually finished reading the post (! oops). I see that you were thinking about cheating, but not quite of this kind. The slogan I would give is something like “cheating by trading accuracy for calibration”. That is, the rule is just supposed to remove the extra phrasing choice from a list to prevent shenanigans from patterned exploitation of this choice.
I now think a challenge to your post would complain that this doesn’t really eliminate the choice—that common wisdom is contradictory enough that I can tweak my phrasing to satisfy your rule and still appear calibrated at 50%-wards probabilities. To be clear, I’m not saying that’s true; the foregoing is just supposed to be a checksum on my understanding.