Second, the method described here offers realistic assessments of the uncertainty of ecological estimates . Reporting the uncertainty of one's conclusions is one of the hallmarks of modern statistics, but it is an especially important problem here. The reason is that ecological inference is an unusual statistical problem in which, under normal circumstances, we never observe realizations of our quantity of interest. For example, since most German citizens who voted for the Nazi party are no longer around to answer hypothetical survey questions, and could hardly be expected to answer them sincerely even if they were, no method will ever be able to fill in the cross-tabulation with certainty. Thus a key component of any solution to this problem is that correct uncertainty estimates be an integral part of all inferences.
Many methods proposed in the literature provide no uncertainty estimates.
Moreover, these estimates are useful since the intervals turn out to be narrower than one might think. Third, the basic model is robust to aggregation bias . Although this book also includes modifications of this basic model to compensate for aggregation bias explicitly, these modifications are often unnecessary. That is, even when the process of aggregation causes existing methods to give answers that bear no relationship to the truth, the method proposed here still usually gives accurate answers. In order to develop an explicit approach to avoiding aggregation bias, I prove that the numerous and apparently conflicting explanations for aggregation bias are mathematically equivalent, even though they each appear to offer very different substantive insights.