An incubator could (Case A) create one person each in rooms numbered from 1 to 100. Or an incubator could (Case B) create 100 people then randomly assign them to these rooms. “The probability that I am in room number 53” has no value in the former case. While it has the probability of 1% for the latter case.
Your two cases seem equivalent to me. To find out where we differ, I’ve created 5 versions of your incubator below. The intent is that Incubator1 implements your Case A; each version is in all relevant ways exactly equivalent to the one below it, and then Incubator5 implements your Case B. Which part of the chain do you disagree with? (A ‘character sheet’ contains whatever raw data you need to make a person, such as perhaps a genome. ‘Roll a character sheet’ means randomly fill in that data in some viable way. Assume we can access a source of true randomness for all rolls/shuffles.)
Incubator1:
For each i<=100:
Roll a character sheet
Create that character in room i
Incubator2:
For each i<=100:
Roll a character sheet and add it to a list
For each i<=100:
Create the i’th listed character in room i
Incubator3:
For each i<=100:
Roll a character sheet and add it to a list
Shuffle the list
For each i<=100:
Create the i’th listed character in room i
Incubator4:
For each i<=100:
Roll a character sheet, add it to a list, and create that character in the waiting area
Shuffle the list
For each i<=100:
Push the person corresponding to the i’th listed character sheet into room i
Incubator5:
For each i<=100:
Roll a character sheet, and create that character in the waiting area
Write down a list of the people standing in the waiting area and shuffle it
Case A and B are different for the same reason as above. A needs to explain why a first-person perspective is a particular person while B does not. If you really think of it, Case B is not even an anthropic problem. It is just about a random assignment of rooms. How I am created, who else is put into the rooms doesn’t change anything.
If we think in terms of frequencies, Case B can be quite easily repeated. I can get into similar room assignments with 99 others again and again. The long-run frequency would be about 1% for every room. But Case A, however, is anthropic. For starters repeating it won’t be so simple. A physical person can’t be created multiple times. It can be repeated by procedures similar to the fission experiment. (Instead of 2 copies each experiment spawns 100 copies.) Then for the same reason, there won’t be a long-run frequency for me.
As for the 5 cases you listed, I would say Case 1 and 2 is the same as A, while cases 4&5 the same as B. But for Case 3 it really depends on your metaphysical position of preexistence. It makes sense for us to say “I naturally know I am this particular person” But can we push this identification back further, from the particular person to the particular character sheet? I don’t think there is a solid answer to it.
Some considerations can include: In theory, can 2 people be created from the same character sheet? If so, the identity of preexistence could not be pushed back. Then Case 3 is definitely like Case A. And that is my reading of the problem. However, if you meant a character sheet and physical person has a one-to-one mirroring relationship. Then saying it is the same as Case B and assigning probabilities to it wouldn’t cause any problems either. At least not in any way I have foreseen.
[case designations added:]
Your two cases seem equivalent to me. To find out where we differ, I’ve created 5 versions of your incubator below. The intent is that Incubator1 implements your Case A; each version is in all relevant ways exactly equivalent to the one below it, and then Incubator5 implements your Case B. Which part of the chain do you disagree with? (A ‘character sheet’ contains whatever raw data you need to make a person, such as perhaps a genome. ‘Roll a character sheet’ means randomly fill in that data in some viable way. Assume we can access a source of true randomness for all rolls/shuffles.)
Incubator1:
For each i<=100:
Roll a character sheet
Create that character in room i
Incubator2:
For each i<=100:
Roll a character sheet and add it to a list
For each i<=100:
Create the i’th listed character in room i
Incubator3:
For each i<=100:
Roll a character sheet and add it to a list
Shuffle the list
For each i<=100:
Create the i’th listed character in room i
Incubator4:
For each i<=100:
Roll a character sheet, add it to a list, and create that character in the waiting area
Shuffle the list
For each i<=100:
Push the person corresponding to the i’th listed character sheet into room i
Incubator5:
For each i<=100:
Roll a character sheet, and create that character in the waiting area
Write down a list of the people standing in the waiting area and shuffle it
For each i<=100:
Push the i’th listed person into room i
Case A and B are different for the same reason as above. A needs to explain why a first-person perspective is a particular person while B does not. If you really think of it, Case B is not even an anthropic problem. It is just about a random assignment of rooms. How I am created, who else is put into the rooms doesn’t change anything.
If we think in terms of frequencies, Case B can be quite easily repeated. I can get into similar room assignments with 99 others again and again. The long-run frequency would be about 1% for every room. But Case A, however, is anthropic. For starters repeating it won’t be so simple. A physical person can’t be created multiple times. It can be repeated by procedures similar to the fission experiment. (Instead of 2 copies each experiment spawns 100 copies.) Then for the same reason, there won’t be a long-run frequency for me.
As for the 5 cases you listed, I would say Case 1 and 2 is the same as A, while cases 4&5 the same as B. But for Case 3 it really depends on your metaphysical position of preexistence. It makes sense for us to say “I naturally know I am this particular person” But can we push this identification back further, from the particular person to the particular character sheet? I don’t think there is a solid answer to it.
Some considerations can include: In theory, can 2 people be created from the same character sheet? If so, the identity of preexistence could not be pushed back. Then Case 3 is definitely like Case A. And that is my reading of the problem. However, if you meant a character sheet and physical person has a one-to-one mirroring relationship. Then saying it is the same as Case B and assigning probabilities to it wouldn’t cause any problems either. At least not in any way I have foreseen.