Abstract. In his 1997 book, King announced “A Solution to the Ecological Inference Problem.” King's method may be tested with data where truth is known. In the test data, his method produces results that are far from truth, and diagnostics are unreliable. Ecological regression makes estimates that are similar to King's, while the neighborhood model is more accurate. His announcement is premature.

Introduction

Before discussing King (1997), we explain the problem of “ecological inference.” Suppose, for instance, that in a certain precinct there are 500 registered voters of whom 100 are Hispanic and 400 are non-Hispanic. Suppose too that a Hispanic candidate gets ninety votes in this precinct. (Such data would be available from public records.) We would like to know how many of the votes for the Hispanic candidate came from the Hispanics. That is a typical ecological-inference problem. The secrecy of the ballot box prevents a direct solution, so indirect methods are used.

This review will compare three methods for making ecological inferences. First and easiest is the “neighborhood model.” This model makes its estimates by assuming that, within a precinct, ethnicity has no influence on voting behavior: In the example, of the ninety votes for the Hispanic candidate, 90 × 100/(100 + 400) = 18 are estimated to come from the Hispanic voters. The second method to consider is “ecological regression,” which requires data on many precincts (indexed by i).