The dual-system estimator, or estimators with a similar underlying set of assumptions and structure, is a widely used approach to estimate the unknown size of a population. Within official statistics its use is linked with population census, while in health applications it is often used to estimate true levels of incidence from imperfect reporting systems; the classic example being work by Sekar and Deming exploring the estimation of births in India in the 1940s. Critical to the implementation of dual-system estimation are the assumptions that the probability of being counted in a source is homogeneous and that the event of being counted in each source is independent. When either of these assumptions fails, the two by two table will have an odds ratio different to one and the dual-system estimator will be biased.