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Does District Magnitude Matter? The Case of Taiwan

Does District Magnitude Matter? The Case of Taiwan

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Carlisle Rainey

January 13, 2012
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  1. The Question Background Data and Methods Results Does District Magnitude

    Matter? The Case of Taiwan Carlisle Rainey Department of Political Science Department of Statistics Florida State University January 13, 2012 Rainey District Magnitude
  2. The Question Background Data and Methods Results Table of Contents

    1 The Question 2 Background Theory Critique 3 Data and Methods Data Posterior Probabilities Bayesian Model Averaging 4 Results Posterior Densities Summary Rainey District Magnitude
  3. The Question Background Data and Methods Results The Key Question

    Does proportional representation cause higher turnout? Rainey District Magnitude
  4. The Question Background Data and Methods Results The Key Question

    Does proportional representation cause higher turnout? • Some authors say “Yes” (Powell 1982, Franklin 2002, Selb 2009). Rainey District Magnitude
  5. The Question Background Data and Methods Results The Key Question

    Does proportional representation cause higher turnout? • Some authors say “Yes” (Powell 1982, Franklin 2002, Selb 2009). • Some authors say “Maybe” (Blais and Dobrzynska 1998, Blais and Aarts 2005, Fornos et al. 2004). Rainey District Magnitude
  6. The Question Background Data and Methods Results Theory Critique Why

    Might Turnout be Higher Under PR? • Disproportional systems leave some voters without representation (Powell 2000, Karp and Banducci 2008). Rainey District Magnitude
  7. The Question Background Data and Methods Results Theory Critique Why

    Might Turnout be Higher Under PR? • Disproportional systems leave some voters without representation (Powell 2000, Karp and Banducci 2008). • Proportional rules gives parties incentive to disperse across the ideological space, making narrow appeals to voters (Cox 1990). Rainey District Magnitude
  8. The Question Background Data and Methods Results Theory Critique Why

    Might Turnout be Higher Under PR? • Disproportional systems leave some voters without representation (Powell 2000, Karp and Banducci 2008). • Proportional rules gives parties incentive to disperse across the ideological space, making narrow appeals to voters (Cox 1990). • Proportional rules create “nationally competitive districts” in which parties have an incentive to mobilize everywhere (Powell 1982, Cox 1999, Selb 2009). Rainey District Magnitude
  9. The Question Background Data and Methods Results Theory Critique Why

    Might Turnout be Higher Under PR? • Disproportional systems leave some voters without representation (Powell 2000, Karp and Banducci 2008). • Proportional rules gives parties incentive to disperse across the ideological space, making narrow appeals to voters (Cox 1990). • Proportional rules create “nationally competitive districts” in which parties have an incentive to mobilize everywhere (Powell 1982, Cox 1999, Selb 2009). In summary, under PR, citizens should be more likely to... 1 feel represented (H2), 2 feel close to a party (H3), 3 be contacted (H4), ...and then vote (H1). Rainey District Magnitude
  10. The Question Background Data and Methods Results Theory Critique Some

    Problems Theoretical • PR reduces the decisiveness of elections (Jackman 1987) • Disproportionality might actually increase the incentive to mobilize (Schram and Sonnemans 1996, Rainey, under review). Rainey District Magnitude
  11. The Question Background Data and Methods Results Theory Critique Some

    Problems Theoretical • PR reduces the decisiveness of elections (Jackman 1987) • Disproportionality might actually increase the incentive to mobilize (Schram and Sonnemans 1996, Rainey, under review). Methodological 1 Most research has focused on testing whether PR increases turnout, not adjudicating among explanations. 2 The methods used in this literature cannot assess the evidence in favor of a null effect. 3 PR systems are different in many ways from majoritarian systems, making it difficult to estimate an unbiased effect. Rainey District Magnitude
  12. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Data Taiwan offers an especially useful case for testing theoretical arguments • substantial variation in district magnitude • national political context held constant Rainey District Magnitude
  13. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Data Taiwan offers an especially useful case for testing theoretical arguments • substantial variation in district magnitude • national political context held constant Survey (CSES) conducted during the 2001 legislative election • the magnitude of each respondent’s district • self-reported turnout • questions tapping whether respondents feel represented, feel close to a party, and were contacted by a party Rainey District Magnitude
  14. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Assessing Evidence for the Null: Posterior Probabilities Given a set of models M = {M1, ..., Mn }, one of which generated the data D, it is possible to assign probabilities to each model. p(Mi |D) = p(D|Mi )p(Mi ) n k=1 p(D|Mk )p(Mk ) These quantities allow us to... 1 assess the relative quality of the model 2 assign probabilities to hypotheses (as opposed to p-values) • P(βmagnitude = 0|D) 3 average estimates across models Rainey District Magnitude
  15. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Model Uncertainty The Problem of Model Specification • I have little prior belief about what the correct model specification is. Rainey District Magnitude
  16. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Model Uncertainty The Problem of Model Specification • I have little prior belief about what the correct model specification is. • Fifteen possible control variables, all occurring causally prior to effect of district magnitude. Rainey District Magnitude
  17. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Model Uncertainty The Problem of Model Specification • I have little prior belief about what the correct model specification is. • Fifteen possible control variables, all occurring causally prior to effect of district magnitude. • Including too many variables can make estimates less precise, including too few can lead to omitted variable bias. Rainey District Magnitude
  18. The Question Background Data and Methods Results Data Posterior Probabilities

    Bayesian Model Averaging Model Uncertainty The Problem of Model Specification • I have little prior belief about what the correct model specification is. • Fifteen possible control variables, all occurring causally prior to effect of district magnitude. • Including too many variables can make estimates less precise, including too few can lead to omitted variable bias. • Inferences are somewhat sensitive to model specification. (215 = 32, 768 possible combinations of control variables.) I explicitly average across inferences, weighting by the posterior probability of each model. Rainey District Magnitude
  19. The Question Background Data and Methods Results Posterior Densities Summary

    A Look at One Model in Detail: Logit Coefficient Estimates for Model of Turnout −0.10 0.05 0.20 0.0 0.6 Age −0.3 0.0 0.3 0.0 0.6 Age.Squared −0.8 −0.2 0.4 0.0 0.6 Male −0.1 0.1 0.3 0.0 0.6 Education 0.0 1.0 0.0 0.6 Married −0.5 0.5 0.0 0.6 Union.Member −0.2 0.0 0.2 0.0 0.6 Household.Income −1.0 0.0 0.0 0.6 Rural −1.0 0.0 1.0 0.0 0.6 Small.Town −0.4 0.2 0.8 0.0 0.6 Suburb −0.5 0.5 0.0 0.6 White.Collar −1.0 0.0 0.0 0.6 Worker −1.5 −0.5 0.5 0.0 0.6 Hakka −0.5 0.5 0.0 0.6 MinNan −1.0 0.5 1.5 0.0 0.6 Mainlander −0.4 0.0 0.0 0.6 log.Magnitude Rainey District Magnitude
  20. The Question Background Data and Methods Results Posterior Densities Summary

    Estimate of the Coefficient for District Magnitude Rainey District Magnitude
  21. The Question Background Data and Methods Results Posterior Densities Summary

    Summary of Results Results for the other outcomes are similar to turnout. (Number in parentheses is percent chance that βmagnitude = 0, conditioning on the data.) 1 feel represented (H2, .02), 2 feel close to a party (H3, .03), 3 be contacted (H4, .03), ...and then vote (H1, .03). Rainey District Magnitude
  22. The Question Background Data and Methods Results Conclusion • The

    literature on electoral rules has asserted that PR increases turnout, but this argument has theoretical contradictions and empirical difficulties. • Using posterior probabilities and the useful case of Taiwan, I find strong evidence that proportional electoral rules do not increase turnout. • I find strong evidence for the null for each of the three mechanisms I test. Rainey District Magnitude