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).
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).