Panel a shows a population of seven people, two of whom have died (shown in gray). A directed edge i → j indicates that i counts j as having died when answering the question, “How many people do you know who have died in the past 12 months?” Panel b shows the same population but redrawn so that each person now appears twice: as someone who reports (left) and as someone who could be reported about (right). People who have died cannot report (they cannot be interviewed). This figure depicts detailed individual reports i → j; but in practice, reports are not typically collected at that level of detail (i.e., we typically would know that person i reports one death, but not that the death was specifically person j). Fortunately, the identity in Eq. (3) requires estimates of aggregate quantities, so this level of detail is not required