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In Bayesianism, every theory has a certain prior probability. Now of course, this can be a very subjective task, and so I am anticipating that there is no correct answer, but am still curious for a response.

Now, certain theories may seem more implausible than others simply because they are necessarily more improbable. For example, it makes sense to give the prior probability of supernaturalism in general a higher or equal value than a specific god. The former contains the latter.

But what about theories that haven’t been tested and yet are differentiated by how plausible they seem. For example, a god who is bored and plays a random draw by people’s names and then decides which person to help that day may seem less plausible and harder to imagine than a god who decides to help someone who did good deeds that day.

Of course, there is no verifiable or testable evidence of either. But should one of these be given a higher or lower prior probability simply by the ease it which it is imagined?

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  • I found it easier to imagine a giant pink rabbit living on Mars than a microscopic purple hyena living on an unnamed planet in a galaxy I have never heard of. Does that make the former more likely? Mar 17, 2023 at 6:47
  • Your examples are hilarious sometimes 😂 I suppose the answer depends on how one defines likely. But if I had to guess, no, they’re equally unlikely Mar 17, 2023 at 7:24
  • The latter of course is far more likely. A cold planet with no water and little atmosphere is unlikely to support rabbits of any color or size. But with near infinite galaxies of planets to develop on, a complex animal that both approximates a hyena and is tiny and purple is reasonably plausible. So Marco’s imagination misled him.
    – Dcleve
    Mar 17, 2023 at 8:41
  • Ha! Cheers, guys! Mar 17, 2023 at 9:04
  • @Dcleve I think his point is that in the case of options we haven’t even confirmed to be possible, it makes no sense to discuss what is more or less likely among them. Mar 17, 2023 at 9:05

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I think that the answer to this question is irreducibly subjective (as some founders of Bayesian statistics such as de Finetti or Ramsey may probably also have said). A probability subjectivist would accept arguments based on coherence, i.e., they would accept that a superset cannot have a smaller probability than a subset, so not all probability assignments are arbitrary, but when it comes to the situation you are asking about, I don't see any logical or objective reason to enforce anything other than your subjective choices.

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