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Either John wrote the song or Paul did. Therefore P(Paul wrote it) either one or zero. That’s not how Bayesian probability works. See https://news.ycombinator

Either John wrote the song or Paul did. Therefore P(Paul wrote it) either one or zero. That’s not how Bayesian probability works. See https://news.ycombinator.com/item?id=17743049 https://news.ycombinator.com/item?id=17743049 https://news.ycombinator.com/item?id=17742927 https://news.ycombinator.com/item?id=17742927 By your logic, every proposition is either true or false, and therefore the concept of probability is useless. Now, can you please explain what it means to calculate that P(Paul wrote it) = 0.018? That depends on their model, which I’m not necessarily defending.

nanis 8y ago
> By your logic, every proposition is either true or false, and therefore the concept of probability is useless. That would be nonsensical interpretation of my logic. In cases where it is possible to conceive of an experiment being repeated in the future, a "degree of belief" interpretation is appealing. If the answer were going to be revealed objectively and someone were taking bets, sure, fine, I'll go along with that. But, don't make an appeal to the Dutch book argument in a unique one-off case where no one has anything at stake other than free publicity which they have chosen to pursue by counting some stuff and dividing those counts by some numbers and stuff.
- antidesitter 8y ago
  In cases where it is possible to conceive of an experiment being repeated in the future That's just the thing: Bayesian probability is emphatically not about an experiment being repeated in the future. That's the frequentist interpretation of probability. But, don't make an appeal to the Dutch book argument in a unique one-off case where no one has anything at stake other than free publicity which they have chosen to pursue by counting some stuff and dividing those counts by some numbers and stuff. ??? The Dutch book argument shows that rational people must have subjective probabilities which behave according to the axioms of probability. I don't see the relevance of your statement here at all, particularly the bits about "anything at stake" and "free publicity". And what are you trying to say by the phrase "counting some stuff and dividing those counts by some numbers and stuff"?
  - nanis 8y ago
    > Bayesian probability is emphatically not about an experiment being repeated in the future. That's the frequentist interpretation of probability. I am saying something different, but this seems like a futile discussion. What does it mean to have P(Paul wrote it) equal to some number in (0,1)? Let's call that number q. Explain what q means in words. If the truth were ever going to be revealed, or if I could conceive of the experiment being repeated in the future, I could explain it as "I would be willing to pay up to $q to buy an asset that pays $1 if Paul wrote it and $0 otherwise." > And what are you trying to say by the phrase "counting some stuff and dividing those counts by some numbers and stuff"? I mean it is very hard for me to take a person seriously who is doing a whole bunch of interviews without even a working paper somewhere. It seems that if you use some arithmetic, people are inclined to accept what you did without questioning whether it makes sense to apply such models in this case. > The Dutch book argument shows that rational people ... You need to do better than just quoting passages from Wikipedia if you want to understand what that means.
    - antidesitter 8y ago
      You just provided a valid interpretation for q. So what’s the problem here? I don’t understand why you’re arguing that q must be 0 or 1, which is nonsense. I don’t object to your comments about the absence of a working paper. You need to do better than just quoting passages from Wikipedia if you want to understand what that means. You’re accusing me of not understanding the Dutch book argument. Do you have any reason for this, or is it just a baseless accusation?
      - nanis 8y ago
        > You just provided a valid interpretation for q. So what’s the problem here? Isn't it obvious that interpretation does not apply in this situation? > You’re accusing me of not understanding the Dutch book argument. It is not an accusation. It is a statement. The Dutch book argument is basically a "no arbitrage" or "no free lunch" argument. Isn't it obvious then that it cannot be used to justify anything where no money is at stake and no bet regarding the outcome can ever be resolved? PS: This will be my last comment in this thread because I get the distinct feeling that I am talking to Eliza instead of a human being.

nanis 8y ago

> By your logic, every proposition is either true or false, and therefore the concept of probability is useless. That would be nonsensical interpretation of my logic. In cases where it is possible to conceive of an experiment being repeated in the future, a "degree of belief" interpretation is appealing. If the answer were going to be revealed objectively and someone were taking bets, sure, fine, I'll go along with that. But, don't make an appeal to the Dutch book argument in a unique one-off case where no one has anything at stake other than free publicity which they have chosen to pursue by counting some stuff and dividing those counts by some numbers and stuff.

antidesitter 8y ago
In cases where it is possible to conceive of an experiment being repeated in the future That's just the thing: Bayesian probability is emphatically not about an experiment being repeated in the future. That's the frequentist interpretation of probability. But, don't make an appeal to the Dutch book argument in a unique one-off case where no one has anything at stake other than free publicity which they have chosen to pursue by counting some stuff and dividing those counts by some numbers and stuff. ??? The Dutch book argument shows that rational people must have subjective probabilities which behave according to the axioms of probability. I don't see the relevance of your statement here at all, particularly the bits about "anything at stake" and "free publicity". And what are you trying to say by the phrase "counting some stuff and dividing those counts by some numbers and stuff"?
- nanis 8y ago
  > Bayesian probability is emphatically not about an experiment being repeated in the future. That's the frequentist interpretation of probability. I am saying something different, but this seems like a futile discussion. What does it mean to have P(Paul wrote it) equal to some number in (0,1)? Let's call that number q. Explain what q means in words. If the truth were ever going to be revealed, or if I could conceive of the experiment being repeated in the future, I could explain it as "I would be willing to pay up to $q to buy an asset that pays $1 if Paul wrote it and $0 otherwise." > And what are you trying to say by the phrase "counting some stuff and dividing those counts by some numbers and stuff"? I mean it is very hard for me to take a person seriously who is doing a whole bunch of interviews without even a working paper somewhere. It seems that if you use some arithmetic, people are inclined to accept what you did without questioning whether it makes sense to apply such models in this case. > The Dutch book argument shows that rational people ... You need to do better than just quoting passages from Wikipedia if you want to understand what that means.
  - antidesitter 8y ago
    You just provided a valid interpretation for q. So what’s the problem here? I don’t understand why you’re arguing that q must be 0 or 1, which is nonsense. I don’t object to your comments about the absence of a working paper. You need to do better than just quoting passages from Wikipedia if you want to understand what that means. You’re accusing me of not understanding the Dutch book argument. Do you have any reason for this, or is it just a baseless accusation?
    - nanis 8y ago
      > You just provided a valid interpretation for q. So what’s the problem here? Isn't it obvious that interpretation does not apply in this situation? > You’re accusing me of not understanding the Dutch book argument. It is not an accusation. It is a statement. The Dutch book argument is basically a "no arbitrage" or "no free lunch" argument. Isn't it obvious then that it cannot be used to justify anything where no money is at stake and no bet regarding the outcome can ever be resolved? PS: This will be my last comment in this thread because I get the distinct feeling that I am talking to Eliza instead of a human being.