Another point to note in the Simulation Argument is that Bostrom’s definitions for the parameters in his formula are inconsistent and lead to erroneous answers.

Bostrom defines the parameters in his formula as:

fp - Fraction of all human-level technological civilizations that survive to reach a posthuman stage

N - Average number of ancestor-simulations run by a posthuman civilization

H - Average number of individuals that have lived in a civilization before it reaches a posthuman stage

Under these definitions Bostrom gives the number of simulated humans as #*fp*N*H. # is the number of real civilizations, it is omitted in Bostrom’s paper because it may be cancelled from the formula for the fraction of simulated individuals.

To illustrate the inconsistency imagine a scenario where there are 10 real civilizations and 5 of these become post-human. The number of individuals that have lived in each of these 5 civilizations before they reached a post-human stage is 1X, 5X, 3X, 16X and 7X respectively. Of these 5 post-human civilizations only the first two run ancestor simulations, the first (with 1X individuals) runs 1000 simulations and the second (with 5X individuals) runs 1000000 simulations.

From the definitions given above we would calculate fp, N and H to be:

fp = 0.5

N = (1000 + 1000000 + 0 + 0 + 0)/5 = 200200

H = (1X + 5X + 3X + 16X + 7X)/5 = 6.4X

As # is 10, Bostrom’s definitions give the number of simulated individuals as 10*0.5*200200*6.4X = 6406400X, but if we do the calculation ourselves then the number of simulated individuals is clearly 1000*1X + 1000000*5X = 5001000X. Therefore there must be an inconsistency somewhere in the definitions given by Bostrom.

The inconsistency arises because the definition of H is wrong. The first obvious error is that Bostrom takes the average over all post-human civilizations, when only two of these actually contribute as the others do not run simulations. Correcting for this would give us a H of (1X + 5X)/2 = 3X and a number of simulated individuals of 3003000X, but we still get a wrong answer because the average should be per simulation not per civilization. Recalculating H in this way gives us:

H = (1X*1000 + 5X*1000000)/(1000 + 1000000) = 4.996004X

and thus we get the correct answer:

Number of simulated individuals = 10*0.5*200200*4.996004X = 5001000X

The above explicitly shows that Bostrom’s use of H as both the average number of individuals per real civilization and the average number of individuals per simulation is entirely improper, if was not completely obvious from the start, as it should have been.