Anthropic prediction for a large toy landscape

The successful anthropic prediction of the cosmological constant depends crucially on the assumption of a. at prior distribution. However, previous calculations for simplified landscape models showed that the prior distribution is staggered, suggesting a conflict with anthropic predictions. Here we analytically calculate the full distribution, including the prior and anthropic selection effects, for a toy landscape model with a realistic number of vacua, N similar to 10(500). We show that it is possible for the fractal prior distribution that we find to behave as an effectively flat distribution in a wide class of landscapes, depending on the regime of parameter space. Whether or not this possibility is realized depends on currently unknown details of the landscape.