One thing that falls out of this post’s framework is that it makes sense to say that one prediction (and in extension, one probability) is better than another, but it doesn’t make sense to talk about the correct probability – unless ‘correct’ is defined as the point of full information, in which case it is usually unattainable.
This is all well and good, but I feel you’ve just rephrased the problem rather than resolving it. Specifically I think you’re saying the better prediction is the one which contains more information. But how can we tell (in your framework) which model contained more information.
If I had to make my complaint more concrete, it would be to ask you to resolve which of “Story 1” and “Story 2″ is more accurate? You seem to claim that we can tell which is better, but you don’t seem to actually do so. (At least based on my reading).
I think there are some arguments but I deliberately didn’t mention any to keep the post non-political. My claim in the post is only that an answer exists (and that you can’t get it from just the outcome), not that it’s easy to find. I.e., I was only trying to answer the philosophical question, not the practical question.
In which case, isn’t there a much shorter argument. “Given an uncertain event there is some probability that event occurs and that probability depends on the information you have about the event”. That doesn’t seem very interesting to me?
To make this framework even less helpful (in the instance of markets) - we can’t know what information they contain. (We can perhaps know a little more in the instance of the presidential markets because we can look at the margin and state markets—BUT they were inconsistent with the main market and also don’t tell you what information they were using).
This is all well and good, but I feel you’ve just rephrased the problem rather than resolving it. Specifically I think you’re saying the better prediction is the one which contains more information. But how can we tell (in your framework) which model contained more information.
If I had to make my complaint more concrete, it would be to ask you to resolve which of “Story 1” and “Story 2″ is more accurate? You seem to claim that we can tell which is better, but you don’t seem to actually do so. (At least based on my reading).
I think there are some arguments but I deliberately didn’t mention any to keep the post non-political. My claim in the post is only that an answer exists (and that you can’t get it from just the outcome), not that it’s easy to find. I.e., I was only trying to answer the philosophical question, not the practical question.
In which case, isn’t there a much shorter argument. “Given an uncertain event there is some probability that event occurs and that probability depends on the information you have about the event”. That doesn’t seem very interesting to me?
To make this framework even less helpful (in the instance of markets) - we can’t know what information they contain. (We can perhaps know a little more in the instance of the presidential markets because we can look at the margin and state markets—BUT they were inconsistent with the main market and also don’t tell you what information they were using).