We examine the effect that agents anchor their perceptions of societal mean incomes on their own incomes. As we show analytically and verify by means of numerical simulation, this self-anchoring implies that even if the sampling of agents is unbiased and fully random, including their own income into their estimate of the average can lead to substantial misperceptions, especially, if the sampling ratio is small. Within a Meltzer–Richard framework, we then demonstrate that self-anchoring leads to a decrease in implemented redistribution.