This is a summary of the GPI Working Paper "Simulation Expectation" by Teruji Thomas. The summary was written by Riley Harris.

At some point in the future we may invent sophisticated simulations. If we do so, we could run millions of simulations of minor variants of the 21st century, each inhabited by simulated people. To those simulated people, it will appear as if they really lived in the 21st century. But that is exactly how our world appears to us, and perhaps we live in a simulation.

Indeed, according to Bostrom (2003) if there are many more simulated than non-simulated people, then we are most likely simulated. However, this argument can only ever be as strong as our belief that there actually are many more simulated than non-simulated people. For example, Bostrom believes there is only about a one-third probability that there really are many more simulated people than non-simulated people, so this argument is compatible with a two-thirds probability that we are not in a simulation. In “Simulation Expectation”, Teruji Thomas develops a novel argument for the claim that we are living in a simulation.

The argument for the simulation hypothesis

Thomas’ argument relies on the concept of a ‘reference class’. To illustrate, suppose I smoke, and I want to know the probability that I’ll develop lung cancer. If I knew that one out of fifteen smokers develop lung cancer, I could use my reference class (people who smoke) to make a prediction (1/15 probability of developing lung cancer). In general, a reference class is a way of assigning an initial probability to ‘things like this’.

Thomas applies this kind of reasoning to our probability of being in a simulation. He suggests that we use the reference class of people who inhabit ‘Earthy’ worlds: that is, people who inhabit minor variations of twenty-first-century earth.

The argument goes like this:

Premise 1: Suppose that we ourselves are non-simulated. Then the expected ratio of simulated to non-simulated people living in Earthy worlds is very high.

Premise 2: The fact that we are living in an Earthy world includes almost all the relevant evidence we have.

Premise 3: Given 1 and 2, the probability that we are living in a simulation is also very high.

Conclusion: Therefore, the probability that we are living in a simulation is very high.

Premise 1 notes that, even though it may be unlikely that our descendants are ever able to create sophisticated simulations of the 21st century, if they do, then they may well create a very large number of simulated worlds broadly like our own. Thus, if we are not simulations (so that base-reality is an Earthy world), then the expected ratio of simulated to non-simulated people in Earthy worlds is very high.

Premise 2 is important because additional evidence could change the resulting probability. In our first example, if a genetic test showed that I had a gene associated with increased lung cancer risk, then the probability that I develop lung cancer would be greater than 1/15. In this case, the fact that we live in a minor variation of twenty-first-century earth includes almost all of the evidence we have about whether or not we live in a simulation. It leaves out personal details such as what I ate for breakfast or the colour of my socks, but these details are almost entirely irrelevant to the question of whether or not we live in a simulation.

The paper contains a mathematical proof of Premise 3. The upshot is that the expected ratio of simulated to non-simulated people in our reference class provides a lower bound to the odds that we live in a simulation. Together, these premises support the conclusion that the probability that we are in a simulation is very high indeed.

Carefully interpret evidence

There is a potential objection to Premises 1 and 2: perhaps we cannot define “Earthy” in a way that includes almost all of the relevant evidence (Premise 2) while also ensuring that the expected ratio of simulated to non-simulated people is high (Premise 1).

Consider the (apparent) fact that our world is more than ten billion years old and was mostly lifeless for many of those billions of years. Even if our descendants create many simulations of our world, it is unlikely that many of those simulated worlds will themselves contain vast empty stretches for billions of years; they would just appear that way.  So, if we include this fact in what it means to be an “Earthy” world, then Premise 1 may well fail. If, however, we exclude this fact from what it means to be an “Earthy” world, then Premise 2 may well fail, because we are excluding an important piece of evidence. One possible way to resolve this is to try to understand our evidence, not in terms of how the world is, but in terms of how the world appears to be. Potentially, we can keep both Premises 1 and 2 if the definition of “Earthy” includes the fact that the world appears to be old and mostly lifeless but doesn’t require the world to actually be that way. This raises some complicated issues.

Because of these considerations, we must carefully interpret any evidence we encounter. Imagine stumbling upon a lab running billions of simulations. Would your new evidence make it likely that you live in a simulation? Bostrom (2006, p. 9) and Greene (2020) think so, but the situation is unclear. If your new evidence is only that the lab appears to be running billions of simulations, then it is unclear which way the new evidence points. On the other hand, most simulations probably do not house their own simulations––so if your new evidence is that the lab really is running billions of simulations, then that could make it less likely that you are in a simulation.

References

Nick Bostrom (2003). Are we living in a computer simulation? The Philosophical Quarterly 53/211.

Nick Bostrom (2006). Do we live in a computer simulation? NewScientist 192/2579.

Preston Greene (2020). The termination risks of simulation science. Erkenntnis 85/2.

Teru Thomas (2021). Simulation Expectation. GPI Working Paper No. 16–2021.