When there are two or more data systems and none of them enumerates the population at an acceptable completeness level, concern about the bias due to underenumeration suggests an estimator which makes joint use of data compiled by the combined imperfect data systems. Conventional dual system estimators are based on the existence of two separate data collection systems. Dual system network estimators assume a main survey and a follow-up quality check survey. The main survey adopts a multiplicity counting rule that combines two mutually exclusive partial counting rules. The people that are enumerated in the main survey are eligible for inclusion in the quality check survey if they are enumerable by both partial counting rules.
Three dual system network estimators are presented in this paper. One was previously proposed by the last author [Proc. Survey Res. Meth. Sect., Am. Stat. Assoc., 340-342 (1979)] and is the natural analogue of the conventional dual system estimator. The two other estimators are proposed as potential improvements, although neither of them is the natural analogue of the conventional dual system estimator. The design effects of the three estimators are compared analytically and empirically with one another, and with those of the single system conventional and network estimators.