How Complete Is the Village Register? A Two-List Estimate with Its Uncertainty, and When the Second List Is Worth Collecting

A village register of births or deaths is usually judged by how it feels — tidy, busy, kept by a conscientious registrar — rather than by a number. This paper computes the number, and its uncertainty, using the two-list method: the register holds n1 events, an independently collected second list holds n2 events, and m events appear on both. From those three counts the Chapman capture–recapture formula estimates the true total, and the register's completeness is the ratio of its count to that total. Under stated planning assumptions (expected counts under independence, a log-transform 95 percent interval, and a working tolerance that an estimate is precise enough to act on when its interval half-width is at most 5 percentage points), a register holding 240 of a true 300 events, checked against an equally complete second list with an overlap of 192, gives an estimated total of 299.94 and a completeness of 80.02 percent with an interval of 77.8 to 82.3 percent — precise enough to act on. The same method in a village of 100 events with a register 60 percent complete gives a half-width of 7.63 points, too wide for the stated tolerance. The decision rule derived from the calculations is stated in terms of overlap: the second list must be large enough to produce an expected overlap of roughly 60 to 160 events across the village sizes tabulated (for example, a second list of 135 events against a register of 240 where the true total is 300), and below an overlap of about 20 events the interval for the total becomes so wide — an upper-to-lower ratio of 1.861 at an overlap of 20, and 3.948 at an overlap of 5 — that the answer should not be quoted as a percentage at all. Dependence between the lists is the larger danger: if the overlap is inflated by only 10 percent above its independence value, the estimated completeness is overstated by 7.92 points, a bias no widening of the interval will reveal. All figures are computed from stated assumptions; no register was examined. SIMULATED, NOT MEASURED.