Both seem true and relevant. You could in fact write P(seems like HoH | simulation) >> P(seems like HoH | not simulation), which leads to the other two via Bayes theorem.
P(simulation | seems like HOH) = P(seems like HOH | simulation)*P(simulation) / (P(seems like HOH | simulation)*P(simulation) + P(seems like HOH | not simulation)*P(not simulation))
Even if P(seems like HoH | simulation) >> P(seems like HoH | not simulation), P(simulation | seems like HOH) could be much less than 50% if we have a low prior for P(simulation). That’s why the term on the right might be wrong—the present text is claiming that our prior probability of being in a simulation should be large enough that HOH should make us assign a lot more than 50% to being in a simulation, which is a stronger claim than HOH just being strong evidence for us being in a simulation.
Agreed, I was assuming that the prior for the simulation hypothesis isn’t very low because people seem to put credence in it even before Will’s argument.
But I found it worth noting that Will’s inequality only follows from mine (the likelihood ratio) plus having a reasonably even prior odds ratio.
people seem to put credence in it even before Will’s argument.
This is kind of tangential, but some of the reasons that people put credence in it before Will’s argument are very similar to Will’s argument, so one has to make sure to not update on the same argument twice. Most of the force from the original simulation argument comes from the intuition that ancestor simulations are particularly interesting. (Bostrom’s trilemma isn’t nearly as interesting for a randomly chosen time-and-space chunk of the universe, because the most likely solution is that nobody ever hade any reason to simulate it.) Why would simulations of early humans be particularly interesting? I’d guess that this bottoms out in them having disproportionately much influence over the universe relative to how cheap they are to simulate, which is very close to the argument that Will is making.
Also, even if one could say P(simulation | seems like HoH) >> P(not-simulation | seems like HoH), that wouldn’t be decision relevant, since t could just be that P(simulation) >> P(not-simulation) in either case. What matters is which observation (seems like HoH or not) renders it more likely that the observer is being simulated.
We have no idea if simulations are even possible! We can’t just casually assert “P(seems like HoH | simulation) > P(seems like HoH | not simulation)”! All that we can reasonably speculate is that, if simulations are made, they’re more likely to be of special times than of boring times.
Did you make a typo here? “if simulations are made, they’re more likely to be of special times than of boring times” is almost exactly what “P(seems like HoH | simulation) > P(seems like HoH | not simulation)” is saying. The only assumptions you need to go between them is that the world is more likely to seem like HoH for people living in special times than for people living in boring times, and that the statement “more likely to be of special times than of boring times” is meant relative to the rate at which special times and boring times appear outside of simulations.
Both seem true and relevant. You could in fact write P(seems like HoH | simulation) >> P(seems like HoH | not simulation), which leads to the other two via Bayes theorem.
Not necessarily.
P(simulation | seems like HOH) = P(seems like HOH | simulation)*P(simulation) / (P(seems like HOH | simulation)*P(simulation) + P(seems like HOH | not simulation)*P(not simulation))
Even if P(seems like HoH | simulation) >> P(seems like HoH | not simulation), P(simulation | seems like HOH) could be much less than 50% if we have a low prior for P(simulation). That’s why the term on the right might be wrong—the present text is claiming that our prior probability of being in a simulation should be large enough that HOH should make us assign a lot more than 50% to being in a simulation, which is a stronger claim than HOH just being strong evidence for us being in a simulation.
Agreed, I was assuming that the prior for the simulation hypothesis isn’t very low because people seem to put credence in it even before Will’s argument.
But I found it worth noting that Will’s inequality only follows from mine (the likelihood ratio) plus having a reasonably even prior odds ratio.
Ok, I see.
This is kind of tangential, but some of the reasons that people put credence in it before Will’s argument are very similar to Will’s argument, so one has to make sure to not update on the same argument twice. Most of the force from the original simulation argument comes from the intuition that ancestor simulations are particularly interesting. (Bostrom’s trilemma isn’t nearly as interesting for a randomly chosen time-and-space chunk of the universe, because the most likely solution is that nobody ever hade any reason to simulate it.) Why would simulations of early humans be particularly interesting? I’d guess that this bottoms out in them having disproportionately much influence over the universe relative to how cheap they are to simulate, which is very close to the argument that Will is making.
Also, even if one could say P(simulation | seems like HoH) >> P(not-simulation | seems like HoH), that wouldn’t be decision relevant, since t could just be that P(simulation) >> P(not-simulation) in either case. What matters is which observation (seems like HoH or not) renders it more likely that the observer is being simulated.
We have no idea if simulations are even possible! We can’t just casually assert “P(seems like HoH | simulation) > P(seems like HoH | not simulation)”! All that we can reasonably speculate is that, if simulations are made, they’re more likely to be of special times than of boring times.
Did you make a typo here? “if simulations are made, they’re more likely to be of special times than of boring times” is almost exactly what “P(seems like HoH | simulation) > P(seems like HoH | not simulation)” is saying. The only assumptions you need to go between them is that the world is more likely to seem like HoH for people living in special times than for people living in boring times, and that the statement “more likely to be of special times than of boring times” is meant relative to the rate at which special times and boring times appear outside of simulations.
And that P(simulation) > 0.
Yep, see reply to Lukas.