buybuydandavis comments on Probability, knowledge, and meta-probability - Less Wrong

38 Post author: David_Chapman 17 September 2013 12:02AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (71)
Tags: decision_theory jaynes multi-armed_bandit strategy probability meta-probability epistemology

Comments (71)

You are viewing a single comment's thread.

Comment author: buybuydandavis 14 September 2013 11:08:54PM *  4 points [-]

Here, a single probability value fails to capture everything you know about an uncertain event. And, it’s a case in which that failure matters.

Of course it doesn't. Who ever said it does? Decisions are made on the basis of expected value, not probability. And your analysis of the first bet ignores the value of the information gained from it in executing your options for further play thereafter.

I think you're just fundamentally confusing the probability of a win on the first coin with the expected long run frequency of wins for the different boxes. Entirely different things.

We can’t be absolutely sure the probability is 0.5.

This statement indicates a lack of understanding of Jaynes, or at least an adherence to his foundations. Probably is assigned by an agent based on information - there is no value that the probability is besides what the agent assigns.

Jaynes specifically analyzes coin flipping, correctly asserting that the probability of the outcome of a coin flip will depend on your knowledge of the relation of the initial states of the coin, the force applied to it, and their relation to the outcome. He even describes a method of controlling the outcome, and I believe shared his own data on executing that method, showing how the frequency of heads/tails could be made to deviate appreciably from 0.5.

Having said that, I've always found Jaynes "inner robot" interesting, and have the feeling the idea has real potential.

Comment author: David_Chapman 14 September 2013 11:46:22PM 0 points [-]

Decisions are made on the basis of expected value, not probability.

Yes, that's the point here!

your analysis of the first bet ignores the value of the information gained from it in executing your options for further play thereafter.

By "the first bet" I take it that you mean "your first opportunity to put a coin in a green box" (rather than meaning "brown box").

My analysis of that was "you should put some coins in the box", exactly because of the information gain.

This statement indicates a lack of understanding of Jaynes, or at least an adherence to his foundations.

This post was based closely on the Chapter 18 of Jaynes' book, where he writes:

Suppose you have a penny and you are allowed to examine it carefully, and convince yourself that it is 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.

Do you think he's saying something different from me here?

Powered by Reddit Powered by Reddit