Anthropic Selection for a Low-Entropy Past

The definition of thermodynamic entropy is dependent on one's assignment of physical microstates to observed macrostates. As a result, low entropy in the distant past could be equivalently explained by selection of a particular observer. In this paper, I make the case that because we observe a low-entropy past everywhere even as we look further and further away, anthropic selection over observers does not explain the non-equilibrium state of the observed cosmos. Under a uniform prior over possible world states, the probability of a non-equilibrium past, given our local observations, decreases to zero as the size of the world tends toward infinity. This claim is not dependent on choice of observer, unless the amount of information used to encode the observer's coarse-graining perception function scales linearly with the size of the world. As a result, for anthropic selection to choose a world like the one we live in, the initial state of a universe with size $N$ must be low-information, having Kolmogorov complexity that does not scale with $N$.