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.

Keywords

RxC contingency tables Mathematical programming Transfer probabilities Split-ticket voting lphom

Get full access to this article

View all access options for this article.

References

Barreto

Collingwood

Garcia-Rios

Oskooii

K. A. R.

. 2022. “Estimating Candidate Support in Voting Rights Act Cases: Comparing Iterative EI and EI-R_C Methods.” Sociological Methods & Research 51:271–304.

Berkelaar

, et al. 2020. lpSolve: Interface to ‘Lp_solve’ v.5.5 to Solve Linear/Integer Programs. R package version 5.6.15. https://CRAN.R-project.org/package = lpSolve.

Cho

W. K. T.

Manski

C. F.

. 2008 “Cross Level/Ecological Inference.” pp. 547–69 in The Oxford Handbook of Political Methodology, edited by Box-Steffensmeier

J. M.

Brady

H. E.

Collier

. New York: Oxford University Press.

Corominas

Lusa

Valvet

M. D.

. 2015. “Computing Voter Transitions: The Elections for the Catalan Parliament, from 2010 to 2012.” Journal of Industrial Engineering and Management 8:122–36.

Duncan

Davis

. 1953. “An Alternative to Ecological Correlation.” American Sociological Review 18:665–6.

Forcina

Pellegrino

. 2019. “Estimation of Voter Transitions and the Ecological Fallacy.” Quality & Quantity 53:1859–74.

Goodman

L. A.

1953. “Ecological Regressions and the Behaviour of Individuals.” American Sociological Review 18:663–4.

Goodman

L. A.

1959. “Some Alternatives to Ecological Correlation.” American Journal of Sociology 64(6):610–25.

Gosnell

H. F.

Gill

N. N.

. 1935. “An Analysis of the 1932 Presidential Vote in Chicago.” The American Political Science Review 29:967–84.

10.

Gosnell

H. F.

Schmidt

M. J.

. 1936. “Factorial and Correlational Analysis of the 1934 Vote in Chicago.” Journal of the American Statistical Association 31:507–18.

11.

Greiner

D. J.

Quinn

K. M.

. 2009. “R × C Ecological Inference: Bounds, Correlations, Flexibility, and Transparency of Assumptions.” Journal of the Royal Statistical Society, A 172:67–81.

12.

Greiner

D. J.

Quinn

K. M.

. 2010. “Exit Polling and Racial Bloc Voting: Combining Individual-Level and RxC Ecological Data.” The Annals of Applied Statistics 4:1774–96.

13.

Haneuse

Wakefiled

. 2004 “Ecological Inference Incorporating Spatial Dependence.” Pp. 266–301 in Ecological Inference. New Methodological Strategies, edited by King

Rosen

Tanner

. New York: Cambridge University Press.

14.

Hawkes

1969. “An Approach to the Analysis of Electoral Swing.” Journal of the Royal Statistical Society, A 132:68–79.

15.

Imai

Khanna

. 2016. “Improving Ecological Inference by Predicting Individual Ethnicity from Voter Registration Records.” Political Analysis 24:263–72.

16.

Imai

Strauss

. 2008. “Bayesian and Likelihood Inference for 2 x 2 Ecological Tables: An Incomplete Data Approach.” Political Analysis 16:41–69.

17.

Irwin

Meeter

. 1969. “Building Voter Transition Models from Aggregate Data.” Midwest Journal of Political Science 13:545–66.

18.

Johnston

R. J.

Hay

A. M.

. 1983. “Voter Transition Probability Estimates: An Entropy-Maximizing Approach.” European Journal of Political Research 11:93–8.

19.

King

1997. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton, NJ: Princeton University Press.

20.

King

Rosen

Tanner

M. A.

. 1999. “Binomial-beta Hierarchical Models for Ecological Inference.” Sociological Methods & Research 28:61–90.

21.

King

Rosen

Tanner

M. A.

. 2004. Ecological Inference. New Methodological Strategies. New York: Cambridge University Press.

22.

Klein

J. M.

2019. Estimation of Voter Transitions in Multi-Party Systems. Quality of Credible Intervals in (hybrid) Multinomial-Dirichlet Models. Master Thesis Dissertation. Ludwig-Maximilians-Universität München.

23.

Klima

Schlesinger

Thurner

P. W.

Küchenhoff

. 2019. “Combining aggregate Data and Exit Polls for the Estimation of Voter Transitions.” Sociological Methods & Research 48:296–325.

24.

Klima

Thurner

P. W.

Molnar

Schlesinger

Küchenhoff

. 2016. “Estimation of Voter Transitions Based on Ecological Inference: An Empirical Assessment of Different Approaches.” AStA - Advances in Statistical Analysis 100:133–59.

25.

Manski

C. F.

2003. Partial Identification of Probability Distributions. New York: Springer-Verlag.

26.

Manski

C. F.

2007. Identification for Prediction and Decision. Cambridge, MA: Harvard University Press.

27.

McCarthy

Ryan

T. M.

. 1977. “Estimates of Voter Transition Probabilities from the British General Elections of 1974.” Journal of the Royal Statistical Society, A 140:78–85.

28.

Ogburn

W. F.

Goltra

. 1919. “How Women Vote.” Political Science Quarterly 34:413–33.

29.

Ogburn

W. F.

Talbot

N. S.

. 1929. “A Measurement of the Factors in the Presidential Election of 1928.” Social Forces 8:175–83.

30.

Park

Hanmer

M. J.

Biggers

D. R.

. 2014. “Ecological Inference Under Unfavorable Conditions: Straight and Split-Ticket Voting in Diverse Settings and Small Samples.” Electoral Studies 36:192–203.

31.

Pavía

J. M.

2022. “ei.Datasets: Real Datasets for Assessing Ecological Inference Algorithms.” Social Science Computer Review 40:247–60.

32.

Pavía, J. M. and C. Aybar. 2020. “Electoral Mobility in the 2019 Elections in the Valencian region.” Debats. Journal on Culture, Power and Society 134:27–51.

33.

Pavía

J. M.

Romero

. 2022. Data Wrangling, Computational Burden, Automation, Robustness and Accuracy in Ecological Inference Forecasting of RxC Tables.

34.

Pavía-Miralles

J. M.

2005. “Forecasts from non-Random Samples: The Election Night Case.” Journal of the American Statistical Association 100:1113–22.

35.

Plescia

De Sio

. 2018. “An Evaluation of the Performance and Suitability of RxC Methods for Ecological Inference with Known True Values.” Quality & Quantity 52:669–83.

36.

Puig

Ginebra

. 2015. “Ecological Inference and Spatial Variation of Individual Behavior: National Divide and Elections in Catalonia.” Geographical Analysis 47:262–83.

37.

Robinson W. S. 1950. “Ecological correlations and the behavior of individuals.” American Sociological Review, 15:351–57.

38.

Romero

Pavía

J. M.

. 2021. “Estimating Vote Party Entries and Exits by Ecological Inference. Mathematical Programming Versus Bayesian Statistics.” BEIO 34:85–97.

39.

Romero

Pavía

J. M.

Martín

Romero

. 2020. “Assessing Uncertainty of Voter Transitions Estimated from Aggregated Data. Application to the 2017 French Presidential Election.” Journal of Applied Statistics 47:2711–36.

40.

Rosen

Jiang

King

Tanner

M. A.

. 2001. “Bayesian and Frequentist Inference for Ecological Inference: The RxC Case.” Statistica Neerlandica 55:134–56.

41.

Tziafetas

1986. “Estimation of the Voter Transition Matrix.” Optimization 17:275–9.

42.

Upton

C. J. G.

1978. “A Note on the Estimation of Voter Transition Probabilities.” Journal of the Royal Statistical Society, A 141:507–12.

43.

van der Ploeg

2008. A Comparison of Different Estimation Methods of Voting Transitions with an Application in the Dutch National Elections. The Hague: Centraal Bureau voor de Statistiek.

44.

Vangrevelinghe

1961. “Étude Statistique Comparée des Résultats des Référendums de 1958 et 1961.” Revue de Statistique Applique 9:83–100.

45.

Wakefield

2004. “Ecological Inference for 2 x 2 Tables (with Discussion).” Journal of the Royal Statistical Society, A 167:385–445.

46.

Zhang

1995. Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment. Technical Report TR96-01. Baltimore County, Baltimore, MD: Department of Mathematics and Statistics, University of Maryland.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

1.65 MB