  The U.S. Census Bureau provides an estimate of the true population as a
supplement to the basic census numbers. This estimate is constructed from data
in a post-censal survey. The overall procedure is referred to as dual system
estimation. Dual system estimation is designed to produce revised estimates at
all levels of geography, via a synthetic estimation procedure. We design three
alternative formulas for dual system estimation and investigate the differences
in area estimates produced as a result of using those formulas. The primary
target of this exercise is to better understand the nature of the homogeneity
assumptions involved in dual system estimation and their consequences when used
for the enumeration data that occurs in an actual large scale application like
the Census. (Assumptions of this nature are sometimes collectively referred to
as the ``synthetic assumption'' for dual system estimation.) The specific focus
of our study is the treatment of the category of census counts referred to as
imputations in dual system estimation. Our results show the degree to which
varying treatment of these imputation counts can result in differences in
population estimates for local areas such as states or counties.
