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Could somebody please convince me that "80% +-20% chance" is a coherent thought.
If I say "there's a 10% ± 5% chance AAPL will increase by $100 today" and you say "there's a 10% chance ± 30% chance AAPL will increase by $100 today" and then it happens, who do you trust more?
For the record I'm definitely not convinced that "80% +- 20% chance" is a coherent thought.
Here's a thought experiment: I give you a coin, which is a typical one and therefore has a 50% chance of landing heads or tails. If I asked you the probability it lands on heads, you'd say 50%, and you'd be right.
Now I give you a different coin. I have told you it is weighted, so that it has an 80% chance of landing on one side and 20% chance of landing on another (but I haven't told you whether or not it favors heads or tails.) If I asked you the probability it lands heads when flipped, you should still say 50%.
That's because probabilities are a measure of your own subjective uncertainty about the set of possible outcomes. Probabilities are not a fact about the universe. (This is trivially true because a hypothetical omniscient being would know with 100% certainty the results of every future coinflip, thereby rendering them, by a certain definition, "nonrandom". But they would still be random to humans.)
My first thought was that I agree with you. The second thought was that you can have a confidence in your confidence. My third thought was that that should baked into your primal estimation, and that if you're saying 80% +/- 20%, you're really saying something like 70%. Does it really make sense to be saying, hey, there's a chance I'm 99% sure, but it's only 10%??
These things really only make sense with repeated results anyway. A single event happens or it doesn't.
If you felt a real need to give more details on your prediction, I think it would be more interesting to give buckets, e.g. I expect the housing market to
5%: shrink > 15%
30%: shrink 5 - 15%
60%: stay flat, changing [-5, +5]
12%: grow 5 - 15%
3% grow > 15%
OTOH, thinking about this more (which makes me think that someone smarter and with more statistics has thought more about this), this still doesn't capture the idea of confidence. What if I don't know what a house is, and you ask me this? Can I really make any meaningful statement? I think I could say 50/50 grows or shrinks, or 90% doesn't change more than 95% (because few things do), but it's hard to capture what it means to have little certainty.
i think if it's a binary choice 50% is exactly right since if you don't know what a house is, no process of reasoning could get you better than a coin flip as to the right answer. Similar if you have N different choices where you can't distinguish between them in any meaningful way.
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