Yes; but then how to work that into the scheme to produce a probability?
I deleted the original comment because I realized that the equations given already give zero weight to an agent who assigns a problem a belief value of .5. That’s because it just multiplies both m0 and m1 by .5.
I do wonder though if you should have some way of distinguishing someone who assigns a probability of .5 for complete ignorance, versus one who assigns a probability of .5 due to massive amounts of relevant evidence that just happens to balance out. But then, you’ll observe the ignorant fellow updating significantly more than the well-informed fellow on a piece of evidence, and can use that to determine the strength of their convictions.
I’ve thought about that. You could use a possible-worlds model, where the ignorant person allows all worlds, and the other person has a restricted set of possible worlds within with p is still .5. If updating then means restricting possible worlds, it should work out right in both cases.
Use a log-based unit, like bits or decibels.
Yes; but then how to work that into the scheme to produce a probability?
I deleted the original comment because I realized that the equations given already give zero weight to an agent who assigns a problem a belief value of .5. That’s because it just multiplies both m0 and m1 by .5.
I do wonder though if you should have some way of distinguishing someone who assigns a probability of .5 for complete ignorance, versus one who assigns a probability of .5 due to massive amounts of relevant evidence that just happens to balance out. But then, you’ll observe the ignorant fellow updating significantly more than the well-informed fellow on a piece of evidence, and can use that to determine the strength of their convictions.
I’ve thought about that. You could use a possible-worlds model, where the ignorant person allows all worlds, and the other person has a restricted set of possible worlds within with p is still .5. If updating then means restricting possible worlds, it should work out right in both cases.