It’s just the simple fact that conditional probability of an event can be different from unconditional one.
Before you toss the coin you can reason only based on priors and therefore your credence is 1⁄2. But when a person hears “Hello”, they’ve observed an event “I was selected from a large crowd” which happens twice as likely when the coin is Tails, therefore they can update on this information and get their credence in Tails up to 2⁄3.
This is exactly as surprising as the fact that after you tossed the coin and observed that it’s Heads suddenly your credence in Heads is 100%, even though before the coin toss it was merely 50%.
‘Observation selection effect’ is another name for ‘conditional probability’ - the probability of an event X, given that I observe it at all or observe it several times.
By the way, there’s an interesting observation: my probability estimate before a coin toss is an objective probability that describes the property of the coin. However, after the coin toss, it becomes my credence that this specific toss landed Heads. We expect these probabilities to coincide.
If I get partial information about the result of the toss (maybe I heard a sound that is more likely to occur during Heads), I can update my credence about the result of that given toss. The obvious question is: can Sleeping Beauty update her credence before learning that it is Monday?
By the way, there’s an interesting observation: my probability estimate before a coin toss is an objective probability that describes the property of the coin.
Don’t say “objective probability”—it’s a road straight to confusion. Probabilities represent your knowledge state. Before the coin is tossed you are indifferent between two states of the coin, and therefore have 1⁄2 credence.
After the coin is tossed, if you’ve observed the outcome, you get 1 credence, if you received some circumstantial evidence, you update based on it, and if you didn’t observe anything relevant, you keep your initial credence.
The obvious question is: can Sleeping Beauty update her credence before learning that it is Monday?
If she observes some event that is more likely to happen in the iterations of the experiment where the coin is Tails than in an iterations of the experiment where the coin is Heads than she lawfully can update her credence.
As the conditions of the experiment restrict it—she, threfore, doesn’t update.
And of course, she shouldn’t update, upon learning that it’s Monday either. After all, Monday awakening happens with 100% probability on both Heads and Tails outcomes of the coin toss.
I think that what I call ’objective probability” represent physical property of the coin before the toss, and also that before the toss I can’t get any evidence about the result the toss. In MWI it would be mean split of timelines. While it is numerically equal to credence about a concrete toss result, there is a difference and SB can be used to illustrate it.
It’s just the simple fact that conditional probability of an event can be different from unconditional one.
Before you toss the coin you can reason only based on priors and therefore your credence is 1⁄2. But when a person hears “Hello”, they’ve observed an event “I was selected from a large crowd” which happens twice as likely when the coin is Tails, therefore they can update on this information and get their credence in Tails up to 2⁄3.
This is exactly as surprising as the fact that after you tossed the coin and observed that it’s Heads suddenly your credence in Heads is 100%, even though before the coin toss it was merely 50%.
‘Observation selection effect’ is another name for ‘conditional probability’ - the probability of an event X, given that I observe it at all or observe it several times.
By the way, there’s an interesting observation: my probability estimate before a coin toss is an objective probability that describes the property of the coin. However, after the coin toss, it becomes my credence that this specific toss landed Heads. We expect these probabilities to coincide.
If I get partial information about the result of the toss (maybe I heard a sound that is more likely to occur during Heads), I can update my credence about the result of that given toss. The obvious question is: can Sleeping Beauty update her credence before learning that it is Monday?
Don’t say “objective probability”—it’s a road straight to confusion. Probabilities represent your knowledge state. Before the coin is tossed you are indifferent between two states of the coin, and therefore have 1⁄2 credence.
After the coin is tossed, if you’ve observed the outcome, you get 1 credence, if you received some circumstantial evidence, you update based on it, and if you didn’t observe anything relevant, you keep your initial credence.
If she observes some event that is more likely to happen in the iterations of the experiment where the coin is Tails than in an iterations of the experiment where the coin is Heads than she lawfully can update her credence.
As the conditions of the experiment restrict it—she, threfore, doesn’t update.
And of course, she shouldn’t update, upon learning that it’s Monday either. After all, Monday awakening happens with 100% probability on both Heads and Tails outcomes of the coin toss.
I think that what I call ’objective probability” represent physical property of the coin before the toss, and also that before the toss I can’t get any evidence about the result the toss. In MWI it would be mean split of timelines. While it is numerically equal to credence about a concrete toss result, there is a difference and SB can be used to illustrate it.