A Bayesian Approach to the Simulation Argument

Abstract: The Simulation Argument posed by Bostrom (2003) suggests that we may be living inside a sophisticated computer simulation. If post-human civilizations eventually have both the capability and desire to generate such Bostrom-like simulations, then the number of simulated realities would greatly exceed the one base reality, ostensibly indicating a high probability that we do not live in said base reality. In this work, it is argued that since the hypothesis that such simulations are technically possible remains unproven, then statistical calculations need to consider not just the number of state spaces, but the intrinsic model uncertainty. This is achievable through a Bayesian treatment of the problem, which is presented here. Using Bayesian model averaging, it is shown that the probability that we are sims is in fact less than 50%, tending towards that value in the limit of an infinite number of simulations. This result is broadly indifferent as to whether one conditions upon the fact that humanity has not yet birthed such simulations, or ignore it. As argued elsewhere, it is found that if humanity does start producing such simulations, then this would radically shift the odds and make it very probable that we are in fact sims.