Open thread, June. 12 - June. 18, 2017

Thomas

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If it's worth saying, but not worth its own post, then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should start on Monday, and end on Sunday.

4. Unflag the two options "Notify me of new top level comments on this article" and "Make this post available under..." before submitting

Sorry, you lost me completely. I didn't prove that P(Heads | Monday) > 1/2 at all.

You had said:

This is in contrast to the standard halfer position, where P(Heads | Monday) > 1/2

Neither of your links to the halfer position shows anyone claiming that. So I assumed you tried to deduce it from the halfer position. The obvious way to deduce it is wrong for the reason I stated.

Could you say which step (1-6) is wrong, if I am Beauty, and I wake up, and I reason as follows?

"CurrentlyMonday" as you have defined it is a per-awakening probability, not a per-experiment probability. So the P(Heads) that you end up computing by those steps is a per-awakening P(Heads). Per-awakening, P(Heads) is 1/3, which indeed is less than 1/2.

The halfer position assumes that the probability that is meaningful is a per-experiment probability.

(If you want to compute a per-experiment probability, you would have to define CurrentlyMonday as something like "the probability that the experiment contains a bet where, at the moment of the bet, it is currently Monday", and step 3 won't work since CurrentlyMonday and CurrentlyTuesday are not exclusive.)

"CurrentlyMonday" as you have defined it is a per-awakening probability

The halfer position assumes that the probability that is meaningful is a per-experiment probability.

To be clear, you're saying that, from a halfer position, "the probability that, when Beauty wakes up, it is currently Monday" is meaningless?

Neither of your links to the halfer position shows anyone claiming that.

Sorry, I wrote that without thinking much. I've seen that position, but it's definitely not the standard halfer position. (It seems to be entirelyus... (read more)