Probability in her various guises comes up a lot at ISF. We cite statistics and percentages, mention things like relative risk, and point to studies with p values to justify our positions. We invoke Bayes and Occam. But I'm often troubled by just what probability is supposed to mean. Is it, for example an estimate of epistemic ignorance only? Or does it say something meaningful (and real) about the actual status of the world? Maybe probability is something more bizarre, like a kind of clock which separates the past (certainty) from the future (uncertain), or maybe it measures entropy. Or maybe it's all just a happy mathematical game without any larger meaning.
If I read last week that Hillary has a 60% chance of winning the election, and I read this week that her chances have improved to 80%, it feels to me like that's a real difference - a factual, measured difference. And yet, after the election, when I know the outcome, it's hard to look back with any seriousness and think those numbers meant much other than I didn't know what the outcome would be.
Here's a problem making the rounds about probability. I mention it not to get the "correct" answer, but as a target to invite conversations about what we should take probability to mean.
Sally rolls two dice (6-sided, assumed fair). She shows one is a six. What is the probability that the other one is a six?
1) Either zero or one.
2) 1/2
3) 1/6
4) 1/11
5) 1/12
6) 1/36
7) Make up another answer or even reject the premise.
I think there are reasonable arguments for each of those answers. Here are a few and I'll leave the rest of the answers for others to champion.
1) The outcome is already determined and in fact, was determined long ago as each cause led to a subsequent effect until a combination of material events plus the laws of nature resulted in the pre-determined outcome. The results are fixed and must be either zero or one, depending on those prior causes. The fact that we don't know the details is irrelevant - only adding an unnecessary subjective element. In the actual world the dice have already been rolled and their state is a matter of certain, historical fact.
2) True, the results were determined, but the question is about my own estimation and state of knowledge. Since I cannot determine between zero or one and have no insight into the prior determinants, I must average the two and state "1/2".
[3) through 5) left for others]
6) (I picked this one before I found it lacking.) The relevant randomizing event is the original roll. Anything after is tainted by agency (Sally's choices). We know that rolling two die will generate 36 possibilities, only one of which is a pair of sixes. Therefore, keeping only the original roll "pristine" we get 1/36.
If I read last week that Hillary has a 60% chance of winning the election, and I read this week that her chances have improved to 80%, it feels to me like that's a real difference - a factual, measured difference. And yet, after the election, when I know the outcome, it's hard to look back with any seriousness and think those numbers meant much other than I didn't know what the outcome would be.
Here's a problem making the rounds about probability. I mention it not to get the "correct" answer, but as a target to invite conversations about what we should take probability to mean.
Sally rolls two dice (6-sided, assumed fair). She shows one is a six. What is the probability that the other one is a six?
1) Either zero or one.
2) 1/2
3) 1/6
4) 1/11
5) 1/12
6) 1/36
7) Make up another answer or even reject the premise.
I think there are reasonable arguments for each of those answers. Here are a few and I'll leave the rest of the answers for others to champion.
1) The outcome is already determined and in fact, was determined long ago as each cause led to a subsequent effect until a combination of material events plus the laws of nature resulted in the pre-determined outcome. The results are fixed and must be either zero or one, depending on those prior causes. The fact that we don't know the details is irrelevant - only adding an unnecessary subjective element. In the actual world the dice have already been rolled and their state is a matter of certain, historical fact.
2) True, the results were determined, but the question is about my own estimation and state of knowledge. Since I cannot determine between zero or one and have no insight into the prior determinants, I must average the two and state "1/2".
[3) through 5) left for others]
6) (I picked this one before I found it lacking.) The relevant randomizing event is the original roll. Anything after is tainted by agency (Sally's choices). We know that rolling two die will generate 36 possibilities, only one of which is a pair of sixes. Therefore, keeping only the original roll "pristine" we get 1/36.
via International Skeptics Forum http://ift.tt/2e3ayO3
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