[Y]ou should be as ready to drop it to 69% as raising it to 71%.
No, you should be as ready to drop it to 69% as raise it to ~70.98%. With rounding, obviously, the above isn’t numerically wrong, but that’s not my objection: it encourages the reader to think of probability updates in percentages as addative, which is wrong.
I take your point about ratios but there is a bigger issue. In many cases the expected change in probability is not symmetrical or uniform.
From the article on conservation of expected evidence: “If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. ”
Say I believed that the Sun went around the earth. Given a new piece of evidence it is likely that it will not change your probability much at all. But there is a slight chance that a new piece of evidence will radically change your probability. It is your weighted probabilities of a change in probability that need to balance.
Example, many people who lost their religious faith suddenly came upon a piece of evidence that caused a drastic change in their probability estimate for the existence of God. [in part this may be due to biases such as ignoring contrary evidence, but not entirely.]
Imagine my wife buys a lottery ticket. My estimate of her chance of winning is very low. My wife runs into the room looking excited and brandishing the ticket, my estimate suddenly goes up a lot. Then when I check the numbers it goes up a lot more. On the other hand if I see the ticked crumpled up in the garbage bin, my estimate goes down only a little (from 1/1000000 to 1/1000000000).
No, you should be as ready to drop it to 69% as raise it to ~70.98%. With rounding, obviously, the above isn’t numerically wrong, but that’s not my objection: it encourages the reader to think of probability updates in percentages as addative, which is wrong.
(edited: fixed my wrong numbers...)
Yes, yes, yes, yes, yes. Speaking as someone who keeps making this mistake despite knowing better, I appreciate the attempt to discourage me from it.
I take your point about ratios but there is a bigger issue. In many cases the expected change in probability is not symmetrical or uniform.
From the article on conservation of expected evidence: “If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. ”
Say I believed that the Sun went around the earth. Given a new piece of evidence it is likely that it will not change your probability much at all. But there is a slight chance that a new piece of evidence will radically change your probability. It is your weighted probabilities of a change in probability that need to balance.
Example, many people who lost their religious faith suddenly came upon a piece of evidence that caused a drastic change in their probability estimate for the existence of God. [in part this may be due to biases such as ignoring contrary evidence, but not entirely.]
Imagine my wife buys a lottery ticket. My estimate of her chance of winning is very low. My wife runs into the room looking excited and brandishing the ticket, my estimate suddenly goes up a lot. Then when I check the numbers it goes up a lot more. On the other hand if I see the ticked crumpled up in the garbage bin, my estimate goes down only a little (from 1/1000000 to 1/1000000000).
Your numbers are still wrong I’m afraid—guessing you mean ~70.98%...
Yes, fixed.