It would be useful to have a summary (at the top or bottom) that this post is mostly about comparing SSA and SIA, and readers familiar with the differences can skim most of it.
IMO, the key is to remember that probability is in the map (or the agent’s head, if you prefer), not the territory. Unless you’re talking about God (who famously doesn’t play dice, but kind of seems to), all probabilities are 1 or 0 - that is the universe you’re in, or it isn’t. Your assignment of probability is based on your prediction of which universe you’re in (ignoring logical uncertainty for this comment). Which means you really need to ask about what future experience OF THE AGENT is being predicted by the probability calculation of the agent.
From the experiment-runner’s perspective, half of players die, and any given player AFTER the experiment, without knowing what group the player is in, has 50% chance of death. From a PLAYER’s perspective, they have a 1⁄36 chance of death if the experiment is still open, and a 0% chance of death if it’s finished and they’re alive to answer the question.
Interesting. Using the snake-creating deity setting, what should I expect as a newly created sightless snake, waiting for my eyes? Suppose that the deity will answer my questions while I wait for the dice roll.
SIA: I expect that the deity has created an indescribably large number of batches, and has not rolled snake eyes yet. I expect that there is a 1⁄36 chance that they will roll snake eyes this time. If they don’t, they will likely roll up more batches, and those probabilities will be pretty normal. And then I’ll end up on a indescribably large world with an indescribable number of snakes, of which 50% are red-eyed.
SSA: I expect that the deity has created several batches of snakes, within the expected bounds of a Poisson distribution with P=1/36. I expect that there is a 50% chance that they will roll snake eyes this time, because while the dice are fair, if the deity rolls snake eyes then I am about 35x more real. And then I’ll end up on a large world with lots of snakes (eg, 2^36), of which just over 50% are red-eyed.
So under SIA the past is shaped by anthropics, and under SSA the future is shaped by anthropics. And whatever happens I get very compelling evidence on the SSA vs SIA question.
If the deity is answering questions, you know it’s before the roll, so it’s clearly 1⁄36. The current size of the population (50% blue-eyed and 50% not-yet-determined) is irrelevant—this game has no upper bound, and past dice outcomes do not change the probability of future ones. This holds as well if you know that you’re in the most recent batch.
The conundrum is if you are a snake whose age is unknown who just doesn’t know their eye color yet. It’s 100% blue if the game is ongoing, and 50% if the game is ended, so the question is “what is the probability that the game has ended”. There’s no uncertainty about that to the deity—they know whether the game is ongoing or ended. There is definitely uncertainty to the player, and it will be resolved when they discover their own eye color.
In this case, I support SSA and would wager 50%. Note that this is a pretty specific setup, and doesn’t apply to even similar-sounding anthropic arguments.
It would be useful to have a summary (at the top or bottom) that this post is mostly about comparing SSA and SIA, and readers familiar with the differences can skim most of it.
IMO, the key is to remember that probability is in the map (or the agent’s head, if you prefer), not the territory. Unless you’re talking about God (who famously doesn’t play dice, but kind of seems to), all probabilities are 1 or 0 - that is the universe you’re in, or it isn’t. Your assignment of probability is based on your prediction of which universe you’re in (ignoring logical uncertainty for this comment). Which means you really need to ask about what future experience OF THE AGENT is being predicted by the probability calculation of the agent.
From the experiment-runner’s perspective, half of players die, and any given player AFTER the experiment, without knowing what group the player is in, has 50% chance of death. From a PLAYER’s perspective, they have a 1⁄36 chance of death if the experiment is still open, and a 0% chance of death if it’s finished and they’re alive to answer the question.
Interesting. Using the snake-creating deity setting, what should I expect as a newly created sightless snake, waiting for my eyes? Suppose that the deity will answer my questions while I wait for the dice roll.
SIA: I expect that the deity has created an indescribably large number of batches, and has not rolled snake eyes yet. I expect that there is a 1⁄36 chance that they will roll snake eyes this time. If they don’t, they will likely roll up more batches, and those probabilities will be pretty normal. And then I’ll end up on a indescribably large world with an indescribable number of snakes, of which 50% are red-eyed.
SSA: I expect that the deity has created several batches of snakes, within the expected bounds of a Poisson distribution with P=1/36. I expect that there is a 50% chance that they will roll snake eyes this time, because while the dice are fair, if the deity rolls snake eyes then I am about 35x more real. And then I’ll end up on a large world with lots of snakes (eg, 2^36), of which just over 50% are red-eyed.
So under SIA the past is shaped by anthropics, and under SSA the future is shaped by anthropics. And whatever happens I get very compelling evidence on the SSA vs SIA question.
Can we find real world situation which already happening and is similar to this game? In that case we can solve SIA vs SSA experimentally.
If the deity is answering questions, you know it’s before the roll, so it’s clearly 1⁄36. The current size of the population (50% blue-eyed and 50% not-yet-determined) is irrelevant—this game has no upper bound, and past dice outcomes do not change the probability of future ones. This holds as well if you know that you’re in the most recent batch.
The conundrum is if you are a snake whose age is unknown who just doesn’t know their eye color yet. It’s 100% blue if the game is ongoing, and 50% if the game is ended, so the question is “what is the probability that the game has ended”. There’s no uncertainty about that to the deity—they know whether the game is ongoing or ended. There is definitely uncertainty to the player, and it will be resolved when they discover their own eye color.
In this case, I support SSA and would wager 50%. Note that this is a pretty specific setup, and doesn’t apply to even similar-sounding anthropic arguments.