Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-09T22:20:46.795Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  04 January 2017

Ron Johnston  and
Charles Pattie
Ron Johnston
Affiliation:
School of Geographical Sciences, University of Bristol, BS8 1SS, UK. email: r.johnston@bristol.ac.uk
Charles Pattie
Affiliation:
Department of Geography, University of Sheffield, Sheffield S10 2TN, UK
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
Research Article
Information
Political Analysis , Volume 8 , Issue 4 , 18 July 2000 , pp. 333 - 345
Copyright
Copyright © 2000 by the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alvarez, R. M., and Nagler, J. 2000. “A New Approach for Modelling Strategic Voting in Multiparty Elections.” British Journal of Political Science 30: 57–75.Google Scholar
Bacharach, B. 1970. Biproportional Matrices and Input-Output Changes. Cambridge, MA: MIT Press.Google Scholar
Banducci, S., Karp, J., and Vowles, J. 1998. “Vote Splitting Under MMP.” In Voters’ Victory: New Zealand's First Election Under Proportional Representation, eds. Vowles, J. et al. Auckland: Auckland University Press, pp. 101–119.Google Scholar
Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. 1975. Discrete Multivariate Analysis. Cambridge, MA: MIT Press.Google Scholar
Boston, J., Levine, S., McLeay, E., and Roberts, N. S. 1998. From Campaign to Coalition: The 1996 MMP Election. Palmerston, North NZ: Dunmore Press.Google Scholar
Burden, B. C., and Kimball, D. C. 1998. “A New Approach to the Study of Ticket Splitting.” American Political Science Review 92: 533–544.Google Scholar
Cleave, N., Brown, P. J., and Payne, C. D. 1995. “Evaluation of Methods for Ecological Inference.” Journal of the Royal Statistical Society, Series A 158: 55–72.CrossRefGoogle Scholar
Cousins, M., and McLeay, E. 1998. “Leaflets, Letterboxes and Litter: Candidates and their Campaigns.” In From Campaign to Coalition: The 1996 MMP Election, eds. Boston, J. et al. Palmerston, North NZ: Dunmore Press, pp. 83–95.Google Scholar
Dempster, A. P., Laird, N. M., and Robinson, D. B. 1977. “Maximum-Likelihood from Incomplete Data via the EM Algorithm.” Journal of the Royal Statistical Society, Series B 39: 1–38.Google Scholar
Evans, S. P. 1973. “A Relationship Between the Gravity Model for Trip Distribution and the Transportation Problem in Linear Programming.” Transportation Research 7: 39–61.Google Scholar
Fraser, E., and Zangouropoulos, N. 1998. “The ACT Campaigns: Wellington Central and Beyond.” In From Campaign to Coalition: The 1996 MMP Election, eds. Boston, J. et al. Palmerston, North NZ: Dunmore Press, pp. 47–60.Google Scholar
Freedman, D. A., Klein, S. P., Sacks, J., Smyth, C. A., and Everett, C. G. 1991. “Ecological Regression and Voting Rights.” Evaluation Review 15: 673–711.Google Scholar
Freedman, D. A., Klein, S. P., Ostland, M., and Roberts, M. 1998. “On ‘Solutions’ to the Ecological Inference Problem.” Journal of the American Statistical Association 93: 1518–1520.Google Scholar
Goodman, L. A. 1953. “Ecological Regression and the Behavior of Individuals.” American Sociological Review 18: 663–664.CrossRefGoogle Scholar
Goodman, L. A. 1959. “Some Alternatives to Ecological Correlation.” American Journal of Sociology 64: 610–625.Google Scholar
Irwin, G., and Meeter, D. 1969. “Building Voter Transition Models from Aggregate Data.” Midwest Journal of Political Science 13: 545–566.CrossRefGoogle Scholar
Jackson, K., and McRobie, A. 1998. New Zealand Adopts Proportional Representation. Ashgate: Aldershot.Google Scholar
Johnston, R. J. 1985. The Geography of English Politics: The 1983 General Election. London: Croom Helm.Google Scholar
Johnston, R. J., and Hay, A. M. 1982. “On the Parameters of Uniform Swing in Single-Member Constituency Electoral Systems.” Environment and Planning A 14: 61–74.Google Scholar
Johnston, R. J., and Hay, A. M. 1983. “Voter Transition Probability Estimates: An Entropy-Maximizing Approach.” European Journal of Political Research 11: 93–98.Google Scholar
Johnston, R. J., and Hay, A. M. 1984. “The Geography of Ticket-Splitting: A Preliminary Study of the 1976 Elections Using Entropy-Maximizing Methods.” The Professional Geographer 36: 291–296.Google Scholar
Johnston, R. J., Hay, A. M., and Rumley, D. 1983. “Entropy-Maximizing Methods for Estimating Voting Data: A Critical Test.” Area 15: 35–41.Google Scholar
Johnston, R. J., Hay, A. M., and Taylor, P. J. 1982. “Estimating the Sources of Spatial Change in Election Results: A Multiproportional Matrix Approach.” Environment and Planning A 14: 951–961.Google Scholar
Johnston, R. J., Hay, A. M., and Rumley, D. 1984. “On Testing for Structural Effects in Electoral Geography, Using Entropy-Maximizing Methods to Estimate Voting Patterns.” Environment and Planning A 16: 233–240.CrossRefGoogle Scholar
Johnston, R. J., and Pattie, C. J. 1991a. “Evaluating the Use of Entropy-Maximising Procedures in the Study of Voting Patterns: 1 Sampling and Measurement Error in the Flow-of-the-Vote Matrix and the Robustness of Estimates.” Environment and Planning A 23: 411–420.Google Scholar
Johnston, R. J., and Pattie, C. J. 1991b. “Tactical Voting in Great Britain in 1983 and 1987: An Alternative Approach.” British Journal of Political Science 21: 95–108.Google Scholar
Johnston, R. J., and Pattie, C. J. 1999. “Constituency Campaign Intensity and Split-Ticket Voting: New Zealand's First Election Under MMP, 1996.” Political Science 51: 164–181.Google Scholar
Johnston, R. J., Pattie, C. J., and Allsopp, J. G. 1988. A Nation Dividing? Britain's Changing Electoral Map 1979–1987. London: Longman.Google Scholar
King, G. 1997. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton, NJ: Princeton University Press.Google Scholar
King, G. 1999. “The Future of Ecological Inference Work: A Reply to Freedman et al.” Journal of the American Statistical Association 94: 352–255.CrossRefGoogle Scholar
Levine, S., and Roberts, N. S. 1998. “Surveying the Snark: Voting Behaviour in the 1996 New Zealand General Election.” In From Campaign to Coalition: The 1996 MMP Election, eds. Boston, J. et al. Palmerston, North NZ: Dunmore Press, pp. 183–198.Google Scholar
McCarthy, C., and Ryan, T. M. 1976. “Party Loyalty at Referenda and General Elections: Evidence from Recent Irish Contests.” Economic and Social Review 7: 279–288.Google Scholar
McCarthy, C., and Ryan, T. M. 1977. “Estimates of Voter Transition Probabilities from the British General Elections of 1974.” Journal of the Royal Statistical Society, Series A 140: 78–85.CrossRefGoogle Scholar
Moser, R. G. 1999. “Electoral Systems and the Number of Parties in Postcommunist States.” World Politics 51: 359–384.Google Scholar
Mosteller, F. 1968. “Association and Estimation in Contingency Tables.” Journal of the American Statistical Association 63: 1–28.Google Scholar
Robinson, W. S. 1950. “Ecological Correlations and the Behavior of Individuals.” American Sociological Review 15: 351–357.Google Scholar
Sarlvik, B., and Crewe, I. 1983. Decade of Dealignment. Cambridge: Cambridge University Press.Google Scholar
Tam Cho, W. K. 1999. “Iff the Assumption Fits … A Comment on the King Ecological Inference Solution.” Political Analysis 7: 143–163.Google Scholar
Vowles, J., Aimer, P., Banducci, S., and Karp, J. (eds.). 1998. Voters’ Victory: New Zealand's First Election Under Proportional Representation. Auckland: Auckland University Press.Google Scholar
Upton, G. J. 1978. “A Note on the Estimation of Voter Transition Probabilities.” Journal of the Royal Statistical Society, Series A 141: 507–512.Google Scholar
Wilson, A. G. 1970. Entropy in Urban and Regional Modelling. London: Pion.Google Scholar
Wilson, A. G. 1981. Geography and the Environment: Systems Analytical Methods. Chichester: John Wiley.Google Scholar
Wilson, A. G., and Bennett, R. J. 1985. Mathematical Methods in Human Geography and Planning. Chichester: John Wiley.Google Scholar