Two interpretations of reports of knowledge of subpopulation sizes

We asked respondents how many people they knew in many subpopulations. These numbers, averaged over large representative samples, should vary proportionally to the size of the subpopulations. In fact, they do not. We give two different interpretations of this finding. The first interpretation notes that the responses are linear in subpopulation size for small subpopulations, but with a non-zero offset, and become noisier for larger subpopulations. Our explanation assumes that respondents both invent and forget members of their networks in the subpopulations, in addition to guessing when the number concerned becomes large. The second interpretation notes that the responses are well described by a power law response, in which the mean number of subpopulation members reported known varies as the square root of the subpopulation size. Despite the apparent implausibility of this, we suggest a psychological mechanism and a model which is able to reproduce the behaviour. Other recall data are shown to have similar properties, thus widening the relevance of the findings.