Unpacking LogM: Toward a More General Theory of Party System Density

1. Unpacking LogM: Toward a More General Theory of Party System Density David Lowery, Simon Otjes, Sergiu Gherghina University of Leiden Arjen van Witteloostuijn University of Antwerp Gabor Peli University of Utrecht Holly Brasher University of Alabama at Birmingham

2. Motivation and Approach An Old Tradition: Parties and Interest Groups Key’s 1942 Politics, Parties, and Pressure Groups Wilson’s 1974 Political Organizations Similarities and Differences: Topics and Theories A Backdoor/Inductive/Incremental Strategy Plan of Discussion The Consensus Model of Party Density Four Tests: Replication and Extension A Comparative Assessment

3. Why So Many (Few) Political Parties? Social Cleavages (Grumm 1958; Lipset & Rokkan, 1997; Rose & Urwin 1970) Electoral Institutions (Duverger 1954; Rae 1967; Lijphart 1990; Riker 1982; Taagepera & Shugart 1993) Emphasis on District Magnitude Generalized Duverger’s Rule: Ns = 1.15 (2 + logM)

4. The Consensus Model (Neto & Cox 1997; Ordeshook & Shvetsova 1994; Cox 1997) Includes Institutions, Cleavage, and their Interaction ENPV/ENPS = a + b1 LogML +b2 ENETH + b3 (LogML * ENETH) But….emphasis on Electoral Institutions & Informed Voters District Magnitude Strategic Voting as Psychological Interpretation Curvilinearity and Extreme Cases The Cross-Sectional Evidence

5. Problem One: Strategic Voting The Plausibility of Strategic Voting “At long last, and despite some flickering dissent…., there now seems to be a near consensus that by anything approaching elite standards most citizens think and know jaw-droppingly little about politics.” (Luskin 2002, 282) The Limits of Strategic Voting: 27 (6) of 54 Cases “Strategic Voting ought to fade out when the district magnitude gets much above five.” (Cox 1997, 100) The Transition from Strategic Voting to ML

6. Problem Two: The Use of LogM LogM Lacks any Theoretical Motivation “Although we might predict that single member districts imply two-party systems, and that, say, 15-member districts might imply four or five parties, it is unreasonable to suppose that 120- or 150-member districts (Israel and the Netherlands) will generate 30 or 40 parties.” (Ordeshook and Shvetsova 1994, 106-107). Whisking Away of Anomalies at Upper End Avoids Key Test Implication of Strategic Voting Missed Chance to Test Strategic Voting Boundary

7. Unfolding LogM Cox & Neto (1997) data / Ordeshook & Shvetsova (1994) model Substitute LogM with 2nd Order Polynomial ENPV/ENPS = a + b1 LogML +b2 ENETH + b3 (LogML * ENETH) ENPV/ENPS = a + b1 ML + b2 ML2 + b3 ENETH + b4 (ML * ENETH) + b5 (ML2 * ENETH) Four Tests Demonstrate Functional Equivalence Explore Nonlinearity with ML < 31 Cases Extend Analysis to ML = 120 and 150 Cases Explore Most Extreme Case: NL

8. Test 1: The Equivalence of Functional Forms

9. Conclusions from Test of Functional Equivalence Both Logged and Polynomial Models Outperform Linear Specifications with Interactions of ML and ENETH Outperform Additive Models Logged and Polynomial Models Generate Very Similar Explained Variance and Predicted Values r of predicted values: ENPV = 0.945 r of predicted values: ENPS = 0.937

10. Predicted Values of Logged & Polynomial Models

11. Test 2: ML 1 to ML 30 with Polynomial Model Focus on Cases with ML < 31 Examine Curvilinearity across inclusive Ranges of ML along Natural Breaks in Values of ML Focus on Key District Magnitude (ML) Variable since it is Doing Most of the Work Run Models and Use Estimates to Generate Predicted Values with ENETH set at Mean

12. The Relative Impact of ENETH and ML

13. The Subset Regressions by Values of ML

14. ML1 to ML 5

15. ML1 to ML 12

16. ML1 to ML 20

17. ML1 to ML 30

18. Combined Predicted Values

19. Combining and Substituting Predicted Values

20. Four Worlds of Party Density ML 1: The World of Duverger’s Law (n= 20) ML 2 to 5: Cox’s World of Fading Strategic Voting (n=6) ML 6 to ML 15: Lijphart’s World of the Generalized M+1 Rule (n=17) ML > than 15: A yet undiscovered world in which neither district magnitude nor strategic voting matter (n=7)

21. An Organization Ecology Interpretation Sigmoid Relationships are the hallmark of organization ecology models (Hannan & Freeman 1977) Application to Wide-Range of Organizations Key Elements of Organization Ecology Models Slow Growth: Strategic Voting as Legitimation Rapid Growth and Positive Density Dependence Stability and Negative Density Dependence Parties as just another type of organization?

22. Test 3: Testing the Model with Extreme Cases Can the model be generalized beyond the data? The Two Extreme Cases of Single National Districts: Israel (ML-120) and the Netherlands (ML-150) Competing Theoretical Expectations Consensus Model: Slow Growth, but Growth Organization Ecology: No Change in Number of Parties after Negative Density Dependence Established

23. The Inconsequentiality of District Magnitude for ML>15

24. Test 4: Explaining Negative Density Dependence The Missing Element of the 4 Worlds of Party System Density We hypothesize that issue agenda space is the critical factor in limiting constraint on party niche space (Belanger & Aarts, 2006; Aarts, Macdonald, & Rabinowitz 1999). In exploring this hypothesis, we change several elements. Cross-Section to Time Series Analysis Focus on Extreme Case of the Netherlands ENPV & ENPS to No. of Parties

25. Why View Issues as Determining Constraint? Voters are poorly informed and inattentive (Converse 1964; DelliCarpini and Keeter 1996; Luskin 2002). The critical resources are issues that allow parties to distinguish themselves (Schlesinger 1984; 1985; Aldrich 1995). “Parties formulate policies in order to win elections rather than win elections to formulate policies.” (Downs 1957, 28) Agenda space is limited (Jones and Baumgartner 2005; Rohrschneider 1993).

26. A Critical Test Implication If issue density matters, then party…. …..party numbers should vary with issue agenda, …..births should expand with agenda-party slack, …..deaths should increase with agenda-party excess. Tested with Netherlands post-War data with time series analysis and event history analysis. 161 Parties Competed from 1946 to 2006 Range from low of 10 to high of 28 Small Parties are Important…. D66, ChristenUnie, PvdV

27. Dutch Parties by No. of Elections Competed, 1946-2006

28. Number of Parties Competing by Election, 1952-2006

29. The Size of the Dutch Issue Agenda

30. Step 1: Calculating Electoral Slack by Estimating No. of Parties in Dutch Elections, 1952 to 2006

31. Number of Actual and Predicted PartiesCompeting by Election, 1952-2006

32. Estimated Slack in Party System, 1952-2006

33. Step 2: Estimation of Party Birth and Deaths Cox Proportional Hazard Model, 1956-2006

34. Implications of Test 4 After party systems reach a certain size (ENPV = 15), institutions and cleavages do not matter. Instead, the size of the issue agenda imposes negative density dependence on party systems. As the size of the issue agenda changes, party births and deaths respond to the changes in carrying capacity of the political system for political parties. Implications for Less Extreme Cases: Examination Party Factionalism (Canon 1978)

35. Conclusion An organization ecology approach accounts for what the consensus model explains. It also accounts or the anomalies that the consensus models fails to account for. It suggests new test implications for the consensus model. And it links the study of the density of political party organizations to a broader theory used to study organizations of all kinds.