Improving Estimates Accuracy of Voter Transitions. Two New Algorithms for Ecological Inference Based on Linear Programming

Abstract

The estimation of RxC ecological inference contingency tables from aggregate data is one of the most salient and challenging problems in the field of quantitative social sciences, with major solutions proposed from both the ecological regression and the mathematical programming frameworks. In recent decades, there has been a drive to find solutions stemming from the former, with the latter being less active. From the mathematical programming framework, this paper suggests a new direction for tackling this problem. For the first time in the literature, a procedure based on linear programming is proposed to attain estimates of local contingency tables. Based on this and the homogeneity hypothesis, we suggest two new ecological inference algorithms. These two new algorithms represent an important step forward in the ecological inference mathematical programming literature. In addition to generating estimates for local ecological inference contingency tables and amending the tendency to produce extreme transfer probability estimates previously observed in other mathematical programming procedures, these two new algorithms prove to be quite competitive and more accurate than the current linear programming baseline algorithm. Their accuracy is assessed using a unique dataset with almost 500 elections, where the real transfer matrices are known, and their sensitivity to assumptions and limitations are gauged through an extensive simulation study. The new algorithms place the linear programming approach once again in a prominent position in the ecological inference toolkit. Interested readers can use these new algorithms easily with the aid of the R package lphom.

An ecological inference approach to the origins of proportional representation

“…The algorithm programmed in the ei.MD. bayes function is based on a hierarchical multinomial-Dirichlet Bayesian model (Rosen et al, 2001), whereas the nslphom algorithm is grounded on linear programming (Pavía and Romero, 2022). Both methods are capable of generating local (precinct, district, or polling station) transition matrices.…”

“…Table 6 summarizes the estimated vote transfers in New Zealand between 1925 and 1928, the last two elections in which the conservative Reform party and the liberal United party competed with each other, before forming an electoral coalition for the 1931 election that would subsequently become the National Party. Source: Compiled by the authors using data from CLEA (Kollman et al, 2019) after adjusting to valid votes the global transfer matrix returned by the nslphom algorithm (Pavía and Romero, 2022) with default options. The correspondences between the main historical labels and the ones employed in this research are: Conservative ↔ Højre; Liberal ↔ Venstre; Socialist ↔ Socialdemokrater.…”

“…The correspondences between the main historical labels and the ones employed in this research are: Conservative ↔ Højre; Liberal ↔ Venstre; Socialist ↔ Socialdemokrater. Source: Compiled by the authors using data from CLEA (Kollman et al, 2019) after applying the nslphom algorithm (Pavía and Romero, 2022) Conservative and liberals in New Zealand appear to be much more substitutes than in Denmark. We estimate that in Denmark in 1913 the conservatives transferred to liberals only one vote for every 25 that they managed to retain from their 1910 electorate, whereas the liberals lost to the conservatives one vote for every six they kept.…”

“…Estimation in percentages a of vote transfers between the NZ General elections of 1925 (by row) and 1928 (by columns). Compiled by the authors using data from http://www.jackvowles.com/nzelect.html after applying the nslphom algorithm(Pavía and Romero, 2022) with default options. The correspondences between the main historical labels and the ones employed in this research are: Conservative ↔ Government;Liberal ↔ Nationalist (1925) or United (1928); Socialist ↔ Labour; and Agrarian ↔ Country.…”

“…Estimation of vote transfers for the NZ General elections of 1925 (by row) and 1928 (by columns) by pairings of parties after restricted to districts where each pair compete. Compiled by the authors using data from http://www.jackvowles.com/nzelect.html after applying the nslphom algorithm(Pavía and Romero, 2022) with default options just considering for each pair of parties the districts where they compete. The correspondences between the main historical labels and the ones employed in this research are: C = Conservative ('Reform') ↔ Government; L = Liberal ↔ Nationalist(1925) orUnited (1928); S = Socialist ↔ Labour; and A = Agrarian ↔ Country.…”