Both X chromosome inactivation and autosomal genomic imprinting generate a functional hemizygosity. Here we consider models that explain the evolution of genomic imprinting and X chromosome inactivation from novel perspectives. Specifically, we suggest that random (in)activation events are common in genes and gene clusters with a low probability of transcription. These generate variability that natural selection has acted on to evolve stable monoallelic expression. Possible selection forces might include a need for dosage compensation and the prevention of biallelic silencing where a total switch off would be lethal. Two different mechanisms can accomplish regular monoallelic expression - genomic imprinting and gene counting.