How Much Livestock Loss Can Hide in a Register: The Audit Interval That Bounds It

A herd register must satisfy the identity stock now equals stock before, plus births and purchases, minus deaths and sales. Any unrecorded loss — an animal stolen, an animal that died unrecorded, an animal sold off the book — shows up only as a gap between the number the register predicts and the number a physical count finds. This paper computes how large that gap can be before it can no longer be explained by counting error alone, under stated assumptions: recorded events are entered without error, a full count of a herd of N animals can be wrong by at most the larger of 2 percent of N and 3 animals, an audit raises no query when the gap is inside that counting error, and the register is corrected to the count at each audit, which renews the available slack. The largest loss that can pass a single audit unnoticed is twice the counting error: 20 animals in a 500-head herd, but 6 animals — 30.0 percent of the herd — in a 20-head herd, because the 3-animal floor dominates at small sizes. Because the slack renews at every reconciliation, a steady unrecorded loss can run at 4.0 percent of the herd per year indefinitely under annual audits of a 500-head herd, and at 16.0 percent per year under quarterly audits: shorter intervals between reconciliations raise, rather than lower, the loss that can pass each year. To hold a steady hidden loss to 2 percent of the herd per year, counting accuracy, not interval, is the binding lever: at annual audits the count must be accurate to 1 percent, and a 20-head herd cannot meet the 2 percent bound at any interval shorter than 15.0 years, so register-keeping alone cannot protect a very small herd. A Monte Carlo check with randomly drawn counting errors found that a steady loss running exactly at the 2 percent bound in a 500-head herd is detected at only 50.59 percent of annual audits, so even a loss at the bound is a coin toss to spot in any given year. All results are computed from the stated assumptions; nothing was counted or measured. SIMULATED, NOT MEASURED.