Good idea. Though since it’s a ratio, you do miss out on a scale factor—In my example, you don’t know whether to scale the heads world by 1⁄3 or the tails world by 3. Or mess with both by factors of 3⁄7 and 9⁄7, who knows?
Scaling by the ratio does successfully help you correct if you want to compare options between two worlds—for example, if you know you would pay 1 in the tails world, you now know you would pay 1⁄3 in the heads world. But if you don’t know something along those lines, that missing scale factor seems like it would become an actual problem.
I think you’re confusing the odds ratio (P(A)/P(¬A) * P(B|A)/P(B|¬A)), which ADT can’t touch, with the update on the odds ratio (P(B|A)/P(B|¬A)), which has to be used with a bit more creativity.
Good idea. Though since it’s a ratio, you do miss out on a scale factor—In my example, you don’t know whether to scale the heads world by 1⁄3 or the tails world by 3. Or mess with both by factors of 3⁄7 and 9⁄7, who knows?
Scaling by the ratio does successfully help you correct if you want to compare options between two worlds—for example, if you know you would pay 1 in the tails world, you now know you would pay 1⁄3 in the heads world. But if you don’t know something along those lines, that missing scale factor seems like it would become an actual problem.
The scale ratio doesn’t matter—you can recover the probabilities from the odds ratios (and the fact that they must sum to one).
I think you’re confusing the odds ratio (P(A)/P(¬A) * P(B|A)/P(B|¬A)), which ADT can’t touch, with the update on the odds ratio (P(B|A)/P(B|¬A)), which has to be used with a bit more creativity.