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> There's no fundamental ontological difference between "give me your likelihood ratios between drawing cards [a and b] as the next draw from this deck of cards

> There's no fundamental ontological difference between "give me your likelihood ratios between drawing cards [a and b] as the next draw from this deck of cards" and "give me your likelihood ratios between finding and not finding a continent in an unexplored part of the world". Can you explain this claim? It seems very clearly false to me, so perhaps we're thinking about things in very different terms here. To me, the extremely obvious and fundamental difference between the two is that we have a very good explanation (to use Deutsch's favorite term for emphasis, although that terminology isn't strictly important here) for why we know the probabilities of various events in a game of cards. Of course, our explanation of why we know those probabilities does depend on some assumptions of our model, namely some things about how the cards are shuffled and dealt, but the explanation doesn't really have anything to do with modeling subjective uncertainty of a particular observer. Sure, it is probably physically possible for some observer to have more certainty, like someone just outside the room with an extremely sensitive radar, but that observer would likely be understood to be violating the rules of the game (just like any card player who cheats using more feasible methods). To me, that's fundamentally different from invoking probability when discussing things like the existence of a specific thing in a specific unexplored part of the world, again assuming we don't have some explanation for why the existence of that thing in that place actually has a probability associated with it.

comp_throw7 5y ago
I'd have a hard time doing better than Jaynes: > Suppose you have a penny and you are allowed to examine it carefully, convince yourself that it's an honest coin; i.e. accurately round, with head and tail, and a center of gravity where it ought to be. Then, you're asked to assign a probability that this coin will come up heads on the first toss. I'm sure you'll say 1/2. > Now, suppose you are asked to assign a probability to the proposition that there was once life on Mars. Well, I don't know what your opinion is there but on the basis of all the things that I have read on the subject, I would again say about 1/2 for the probability. But, even though I have assigned the same "external" probabilities to them, I have a very different "internal" state of knowledge about those propositions. > To see this, imagine the effect of getting new information. Suppose we tossed the coin 5 times and it comes up tails every time. You ask me what's my probability for heads on the next throw; I'll still say 1/2. But if you tell me one more fact about Mars, I'm ready to change my probability assignment completely. There is something which makes my state of belief very stable in the case of the penny, but very unstable in the case of Mars. Source: https://books.google.com/books?id=tTN4HuUNXjgC&pg=PA553&lpg=PA553#v=onepage&q&f=false https://books.google.com/books?id=tTN4HuUNXjgC&pg=PA553&lpg=... Ultimately it's a question of how much each bit of evidence would cause you to update (that is, difference of degree, rather than kind).
- tshaddox 5y ago
  But both of those cases are concerning the “Bayesian epistemology” side of things, not using probability to reason about how to bet in games of chance with well-established rules and mechanics. The usage of probability Deutsch is approving of is the latter, and is unrelated to a particular observer’s level of confidence that the cards are designed fairly or that the dealer and other players are playing fairly.
- mhb 5y ago
  > Ultimately it's a question of how much each bit of evidence would cause you to update (that is, difference of degree, rather than kind). Isn't this only because you have strong priors for the coin and weak ones for Mars life? Suppose you didn't have your example's information about the coin. Then the situations are the same and a new piece of evidence in either case (e.g., discovering whether the coin is round, has two heads, or where its center of gravity is).
  - deleted 5y ago
    [deleted]
  - lisper 5y ago
    There is no such thing as a "strong" prior or a "weak" prior. A prior is jut a number between 0 and 1. But the coin example is really not very apt because there is potential information that will change your belief about the coin. For example, you might discover that the coin is magnetic, and there is an external field being generated somewhere in just the right way to make the coin land heads every time. Or something like that. Whatever the case, if you get (say) 100 heads in a row you should start to have some serious doubts about your initial analysis of the situation.
    - unholiness 5y ago
      But ultimately, it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? So, the prior which is strong/weak is the probability distribution of probability distributions. There is a <<1% chance that I will ever believe there is a >90% chance of flipping heads. But there is a much greater probability that I will one day believe there is a >90% chance of life on Mars. What terminology would you use to describe that, if not strong/weak priors?

comp_throw7 5y ago

I'd have a hard time doing better than Jaynes: > Suppose you have a penny and you are allowed to examine it carefully, convince yourself that it's an honest coin; i.e. accurately round, with head and tail, and a center of gravity where it ought to be. Then, you're asked to assign a probability that this coin will come up heads on the first toss. I'm sure you'll say 1/2. > Now, suppose you are asked to assign a probability to the proposition that there was once life on Mars. Well, I don't know what your opinion is there but on the basis of all the things that I have read on the subject, I would again say about 1/2 for the probability. But, even though I have assigned the same "external" probabilities to them, I have a very different "internal" state of knowledge about those propositions. > To see this, imagine the effect of getting new information. Suppose we tossed the coin 5 times and it comes up tails every time. You ask me what's my probability for heads on the next throw; I'll still say 1/2. But if you tell me one more fact about Mars, I'm ready to change my probability assignment completely. There is something which makes my state of belief very stable in the case of the penny, but very unstable in the case of Mars. Source: https://books.google.com/books?id=tTN4HuUNXjgC&pg=PA553&lpg=PA553#v=onepage&q&f=false https://books.google.com/books?id=tTN4HuUNXjgC&pg=PA553&lpg=... Ultimately it's a question of how much each bit of evidence would cause you to update (that is, difference of degree, rather than kind).

tshaddox 5y ago
But both of those cases are concerning the “Bayesian epistemology” side of things, not using probability to reason about how to bet in games of chance with well-established rules and mechanics. The usage of probability Deutsch is approving of is the latter, and is unrelated to a particular observer’s level of confidence that the cards are designed fairly or that the dealer and other players are playing fairly.
mhb 5y ago
> Ultimately it's a question of how much each bit of evidence would cause you to update (that is, difference of degree, rather than kind). Isn't this only because you have strong priors for the coin and weak ones for Mars life? Suppose you didn't have your example's information about the coin. Then the situations are the same and a new piece of evidence in either case (e.g., discovering whether the coin is round, has two heads, or where its center of gravity is).
- deleted 5y ago
  [deleted]
- lisper 5y ago
  There is no such thing as a "strong" prior or a "weak" prior. A prior is jut a number between 0 and 1. But the coin example is really not very apt because there is potential information that will change your belief about the coin. For example, you might discover that the coin is magnetic, and there is an external field being generated somewhere in just the right way to make the coin land heads every time. Or something like that. Whatever the case, if you get (say) 100 heads in a row you should start to have some serious doubts about your initial analysis of the situation.
  - unholiness 5y ago
    But ultimately, it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? So, the prior which is strong/weak is the probability distribution of probability distributions. There is a <<1% chance that I will ever believe there is a >90% chance of flipping heads. But there is a much greater probability that I will one day believe there is a >90% chance of life on Mars. What terminology would you use to describe that, if not strong/weak priors?