Ecological Inference and Entropy-Maximizing: An Alternative Estimation Procedure for Split-Ticket Voting

Abstract

Publication of King's A Solution to the Ecological Inference Problem has rekindled interest in the estimation of unknown cell values in two- and three-dimensional matrices from knowledge of the marginal sums. This paper outlines an entropy-maximizing (EM) procedure which employs more constraints than King's EI method and produces mathematical rather than statistical procedures: the estimates are maximum-likelihood values. The mathematics are outlined, and the procedure's use illustrated with a study of ticket-splitting at New Zealand's first (1996) general election using the mixed-member proportional representation system, for which official figures provide a check against the EM estimate of the number voting a straight party ticket in each constituency.