For example, you should definitely not end up assigning equal probabilities to the following three events -
Strigli wins the game.
It rains immediately after the match is over.
Strigli wins the game AND it rains immediately after the match is over.
I am not sure if your scheme ensures that this does not happen
I just wanted to note that it is actually possible to do that, provided that the questions are asked in order (not simultaneously). That is, I might logically think that the answer to (1) and (2) is true with 50% probability after I’m asked each question. Then, when I’m asked (3), I might logically deduce that (3) is true with 50% probability — however, this only means that after I’m asked (3), the very fact that I was asked (3) caused me to raise my confidence that (1) and (2) are true. It’s a fine point that seems easy to miss.
On a somewhat related point, I’ve looked at the entire discussion and it seems to me the original question is ill-posed, in the sense that the question, with high probability, doesn’t mean what the asker thinks it means.
Take For example, let’s say you are suddenly sent to the planet Progsta and a Sillpruk comes and asks you whether the game of Doldun will be won by the team Strigli. The question is intended to prevent you from having any prior information about its subject.
However, what it means is just that before you are asked the question, you don’t have any information about it. (And I’m not even very sure about that.) But once you are asked the question, you received a huge amount of information: The very fact that you received that question is extremely improbable (in the class of “what could have happened instead”). Also note that it is vanishingly more improbable than, say, being asked by somebody on the street, say, if you think his son will get an A today.
“Something extremely improbable happens” means “you just received information”; the more improbable it was the more information you received (though I think there are some logs in that relationship).
So, the fact you are suddenly sent to the planet Progsta and a Sillpruk comes and asks you whether the game of Doldun will be won by the team Strigli brings a lot of information: space travel is possible within one’s lifetime, aliens exist, aliens have that travel technology, aliens bring people to their planets, aliens can pose a question to somebody just brought to their question, they live on at least one planet, they have something they translate as “game” in English, they have names for planets, individuals, games and teams, they translate those names in some particular English-pronounceable (or -writable, depends on how the question was asked) form.
More subtly, you think that Sillpruk came to you and asked you a question; this implies you have good reason to think that the events should be interpreted as such (rather than just, say, a block of matter arrived in front of you, and it made some sounds. The class of events “aliens take you to their planets and ask you a question” is vastly larger than “the same, but you realize it”.
tl;dr: I guess what I mean is that “what priors you use for a question you have no idea about” is ill formed, because it’s pretty much logically impossible that you have no relevant information.
I just wanted to note that it is actually possible to do that, provided that the questions are asked in order (not simultaneously). That is, I might logically think that the answer to (1) and (2) is true with 50% probability after I’m asked each question. Then, when I’m asked (3), I might logically deduce that (3) is true with 50% probability — however, this only means that after I’m asked (3), the very fact that I was asked (3) caused me to raise my confidence that (1) and (2) are true. It’s a fine point that seems easy to miss.
On a somewhat related point, I’ve looked at the entire discussion and it seems to me the original question is ill-posed, in the sense that the question, with high probability, doesn’t mean what the asker thinks it means.
Take For example, let’s say you are suddenly sent to the planet Progsta and a Sillpruk comes and asks you whether the game of Doldun will be won by the team Strigli. The question is intended to prevent you from having any prior information about its subject.
However, what it means is just that before you are asked the question, you don’t have any information about it. (And I’m not even very sure about that.) But once you are asked the question, you received a huge amount of information: The very fact that you received that question is extremely improbable (in the class of “what could have happened instead”). Also note that it is vanishingly more improbable than, say, being asked by somebody on the street, say, if you think his son will get an A today.
“Something extremely improbable happens” means “you just received information”; the more improbable it was the more information you received (though I think there are some logs in that relationship).
So, the fact you are suddenly sent to the planet Progsta and a Sillpruk comes and asks you whether the game of Doldun will be won by the team Strigli brings a lot of information: space travel is possible within one’s lifetime, aliens exist, aliens have that travel technology, aliens bring people to their planets, aliens can pose a question to somebody just brought to their question, they live on at least one planet, they have something they translate as “game” in English, they have names for planets, individuals, games and teams, they translate those names in some particular English-pronounceable (or -writable, depends on how the question was asked) form.
More subtly, you think that Sillpruk came to you and asked you a question; this implies you have good reason to think that the events should be interpreted as such (rather than just, say, a block of matter arrived in front of you, and it made some sounds. The class of events “aliens take you to their planets and ask you a question” is vastly larger than “the same, but you realize it”.
tl;dr: I guess what I mean is that “what priors you use for a question you have no idea about” is ill formed, because it’s pretty much logically impossible that you have no relevant information.