If there is some entity that is taking some large number of people, and then selecting one of those people to decide the fate of all the rest, your prior that you-in-particular are the one that the entity selected should scale with the number of people in the group. If the group contains 3^^^3 people, you need enough evidence to overwhelm the 1/3^^^3 prior that you in particular have been singled out as special within that group.
I find this confusing. My actual strength of belief now that I can tip an outcome that affects at least 3^^^3 other people is a lot closer to 1/(1000000) than 1/(3^^7625597484987). My justification is that while 3^^^3 isn’t a number that fits into any finite multiverse, the universe going on for infinitely long seems kinda possible and anthropic reasoning may not be valid here (I added 10x in case it is) and I have various ideas. The difference in those two probabilities is large (to put it mildly), and significant (one is worth thinking about and the other isn’t). How to resolve this?
Let’s consider those 3^^^3 other people. Choose one of those people at random. What’s your strength of belief that that particular person can tip an outcome that affects > 0.0001% of those 3^^^3 other people?
Putting it another way: do you expect that the average beliefs among those 3^^^3 people would be more accurate if each person believed that there was a 1/3^^^3 chance that they could determine the fate of a substantial fraction of the people in their reference class, or if each person believed there was a 1/1000000 chance that they could determine the fate of a substantial fraction of the people in their reference class?
the universe going on for infinitely long seems kinda possible
I think in infinite universes you need to start factoring in stuff like the simulation hypothesis.
If there is some entity that is taking some large number of people, and then selecting one of those people to decide the fate of all the rest, your prior that you-in-particular are the one that the entity selected should scale with the number of people in the group. If the group contains 3^^^3 people, you need enough evidence to overwhelm the 1/3^^^3 prior that you in particular have been singled out as special within that group.
I find this confusing. My actual strength of belief now that I can tip an outcome that affects at least 3^^^3 other people is a lot closer to 1/(1000000) than 1/(3^^7625597484987). My justification is that while 3^^^3 isn’t a number that fits into any finite multiverse, the universe going on for infinitely long seems kinda possible and anthropic reasoning may not be valid here (I added 10x in case it is) and I have various ideas. The difference in those two probabilities is large (to put it mildly), and significant (one is worth thinking about and the other isn’t). How to resolve this?
Let’s consider those 3^^^3 other people. Choose one of those people at random. What’s your strength of belief that that particular person can tip an outcome that affects > 0.0001% of those 3^^^3 other people?
Putting it another way: do you expect that the average beliefs among those 3^^^3 people would be more accurate if each person believed that there was a 1/3^^^3 chance that they could determine the fate of a substantial fraction of the people in their reference class, or if each person believed there was a 1/1000000 chance that they could determine the fate of a substantial fraction of the people in their reference class?
I think in infinite universes you need to start factoring in stuff like the simulation hypothesis.
This line of reasoning is a lot like the Doomsday argument.