1. The Logic of Pre-Electoral Coalition Formation SONA NADENICHEK GOLDER Florida State University

2. Question  Under what conditions are pre-electoral coalitions likely to form? Electoral coalitions formed in the 2002 legislative elections in France and Germany but not in the Netherlands. Why?

3. Definitions Most parties who wish to exercise executive power are forced to enter some type of coalition. Parties can form coalitions: After elections (government coalitions). Before elections (pre-electoral coalitions).

4. Definitions A pre-electoral coalition is a collection of parties that do not compete independently in an election. Rather, they publicly agree to coordinate their campaigns by running joint candidates/lists or agreeing to enter government together following the election. Criterion I: An electoral coalition must be publicly stated. Criterion II: Member parties in an electoral coalition cannot compete in elections as truly independent entities. Criterion III: The electoral coalition must be at the national level.

5. Types of Electoral Coalitions Pre-Electoral Coalition TypeDegree of Electoral Coordination Nomination Agreement Joint Lists Dual Ballot Instructions Vote Transfer Instructions Public Commitment to Govern Together

6. Why do we care?  Electoral outcomes  Policy implications  Normative implications  Commonplace

7. Some Figures Data from 19 West European countries 1946-2002  Average of 11 electoral coalitions at any one time.  Average electoral coalition size is 2.6.  25% of these coalitions end up in government.  1/3 of written government coalition agreements based on pre-electoral agreements (Müller & Strøm).

8. Coalition Literature

9. Government Coalition Literature Austin-Smith & Banks (1988) Laver & Schofield (1988) Baron & Ferejohn (1989) Laver & Shepsle (1990) Strøm, Budge & Laver (1994) Lupia & Strøm (1995) Merlo (1997), Warwick (1999) Diermeier et al. (1999, 2003) Warwick & Druckman (2001, 2006) Martin & Vanberg (2003) Etc., etc… See Laver (1998) in Annual Review of Political Science for an overview of models. See Martin & Stevenson (2001) for an empirical analysis of the main hypotheses in the literature. See Müller & Strøm (2000), Coalition Governments in Western Europe for case studies.

10. Electoral Coalition Literature Powell (2000); Kaminski (2001) “One area that cries out for more serious theoretical and empirical work is the appearance of announced pre- electoral coalitions between political parties. We know too little about the origins of such coalitions...” Powell (2000, p. 247)

11. What determines electoral coalition formation?

12. State of the Art  Disproportionality Story “The more disproportional the electoral system, the greater the incentives for pre-electoral alliances” Strom, Budge & Laver (1994, p. 316)  Signaling Story No empirical tests

13. State of the Art: An Empirical Test 405 legislative elections, 25 countries, 1946-2002 Disproportionality  Electoral coalitions are more likely to form and be successful in disproportional electoral systems so long as there is a sufficiently large number of parties. Signaling 

14. State of the Art: Limitations  Costs of electoral coalition formation Ideological and distributional issues  Within-country temporal variation  No bargaining model

15. Theory

16. Bargaining Model  Just as with government coalitions, electoral coalitions emerge from a bargaining process. There are some differences... Government coalitions cannot affect the probability of electoral victory, but pre-electoral coalitions can. Ideological compatibility constraint stronger for electoral coalitions than government coalitions.

17. What does the bargaining model look like?

18.  Actors:  Party A, Party B (Potential Coalition Partners)  Non-Strategic Opposition Party  Party leaders care about:  Office  Policy  Decision:  Party A and Party B must decide whether to form an electoral coalition or run separately.

19. Timeline for Bargaining Game Period 1 Period 2 (No) Party A makes an offer (Yes) Party B accepts (Yes) PEC (No) Party A accepts (Yes) PEC (No) No PECParty B makes an offer (Yes) (No) No PECParty A accepts (Yes) PEC (No) No PEC Party B makes an offer (Yes) (No) No PEC

20. Bargaining Model  Party leaders will form an electoral coalition whenever the expected utility from an agreement is greater than the expected utility from running alone (reservation price).

21. Payoffs Probability of winning and losing:  Probability that you enter government running divided (P i-d ).  Probability that you enter government running united (P t u ), where P 1 u > P 2 u.

22. Payoffs Office Benefits (S)  If parties form an electoral coalition, they divide the office benefits (o 1 A,1-o 1 A ) or (o 2 B,1-o 2 B ).  If parties do not form an electoral coalition but still enter government, they receive share s i of the office benefits, where s i =seats i /(seats i +seats j ).

23. Payoffs Policy  If not in government, you suffer utility loss from having opposition set policy (λ i-opp ), where λ i-opp = - (P i – P opp ) 2  If in government as electoral coalition, you suffer utility loss from coalition policy λ i-pec, where 1. λ i-pec = -(P i –P pec ) 2 2. P pec = p A +s uB |p A -p B | or P pec = p B -s uA |p A -p B | 3. S uA = seats A /(seats A +seats B ) and S uB = seats B /(seats A +seats B )

24. Actors, Actions, and Payoffs  If A makes offer and B accepts in Period 1 P u 1 (o A 1 – λ A-PEC ) - λ A-OPP (1-P u 1 ) ; P u 1 ((1- o A 1 ) – λ B-PEC ) - λ B-OPP (1-P u 1 )  If B rejects A’s offer in Period 1, and A accepts B’s offer in Period 2 P u 2 (o B 2 – λ A-PEC ) - λ A-OPP (1-P u 2 ) ; P u 2 ((1- o B 2 ) – λ B-PEC ) - λ B-OPP (1-P u 2 ) (same payoffs if A makes no offer in Period 1, and A accepts B’s offer in Period 2)  If neither actor makes an offer in either period P A-d (s A -λ A-GOV ) - λ A-OPP (1-P A-d ) ; P B-d (s B -λ B-GOV ) - λ B-OPP (1-P B-d ) (same payoffs if offers are made, but rejected)

25. Equilibria  Depending on parameter values, 3 possible sub- game perfect Nash equilibria in this game.  In two equilibria, electoral coalitions form in the first round.  In one equilibrium, electoral coalitions never form.

26. Comparative Statics The probability of electoral coalition formation increases when:  Ideological distance between coalition partners (λ AB ) decreases.  Ideological distance to opposition (λ i-opp ) increases, so long as coalition is beneficial (P t u > P t i-d ).  Probability that coalition wins (P 1 u, P 2 u ) increases.  Probability that party wins running alone (P i-d ) decreases.

27. What does the model get us?  Surprising result  Party system polarization does not have an unconditional effect on electoral coalition formation.

28. Is this a Good Explanation?

29. Hypothesis 1 The probability of electoral coalition formation increases when:  Ideological distance between coalition partners ( λ AB ) decreases. Hypothesis 1  Pre-electoral coalitions are less likely to form as the ideological distance between potential coalition members increases.

30. Hypotheses 2 and 3 The probability of electoral coalition formation increases when:  Ideological distance to opposition ( λ i-opp ) increases, so long as coalition is beneficial (P t u > P t i-d ). Hypotheses 2 and 3  Party system polarization increases the likelihood of electoral coalitions when the electoral system is sufficiently disproportional.  An increase in the disproportionality of the electoral system will increase the probability of forming a pre-electoral coalition. This positive effect should be stronger when the party system is polarized.

31. Hypothesis 4 The probability of electoral coalition formation increases when:  Probability that coalition wins (P 1 u, P 2 u ) increases.  Probability that party wins running alone (P i-d ) decreases. Hypothesis 4  The probability that an electoral coalition forms is a quadratic function of the size of the potential electoral coalition. It should be increasing in the first term (size) and decreasing in the second term (size 2 ).

32. Hypothesis 5 Hypothesis 4 Hypothesis 5  If the expected coalition size is sufficiently large, then pre- electoral coalitions are less likely to form if there is an asymmetric distribution of electoral strength among the potential coalition parties.

33. Data  292 legislative elections in 20 advanced industrialized parliamentary democracies between 1946 and 1998.

34. Data  292 legislative elections in 20 advanced industrialized parliamentary democracies between 1946 and 1998.  Dyadic format  4,460 potential two-party coalitions.  234 potential coalitions actually formed (5%)  Pre-electoral coalitions formed prior to 44% of elections in dataset

35. Specification  Random-Effects Probit Model PEC* = β 0 + β 1 Incompatibility + β 2 Polarization + β 3 Threshold + β 4 Polarization*Threshold + β 5 Coalition Size+ β 6 Coalition Size 2 + β 7 Asymmetry + β 8 Asymmetry*Coalition Size + ε

36. Results

37. RegressorModel 1 (random effects)Model 2 Ideological Incompatibility-0.007* (0.002) -0.005* (0.002) Polarization0.002 (0.004) -0.001 (0.02) Electoral Threshold0.026* (0.01) 0.021* (0.005) Polarization*Electoral Threshold0.0003 (0.0003) 0.0002 (0.0001) Coalition Size0.043* (0.01) 0.041* (0.008) Coalition Size 2 -0.0005* (0.0001) -0.0004* (0.0001) Asymmetry-0.144 (0.286) -0.01 (0.22) Asymmetry*Coalition Size-0.025* (0.008) -0.024* (0.006) Constant-2.46* (0.29) -2.10* (0.18) N Log Likelihood 3495 -613.49 3495 -663.95 Dependent Variable: Pre-Electoral Coalition (0,1) * p < 0.05 (two-tailed)

38. Interaction Terms in Non-Linear Models: An Aside  Imagine I have some conditional hypothesis whereby some variable Z modifies the effect of X on Y.  One question we might ask is how the value of Z modifies the effect of X on Y.  What is ? We refer to this as the “interaction effect”.

39. Interaction Terms in Non-Linear Models: An Aside  OLS World  Y = β 0 + β 1 X + β 2 Z + β 3 XZ + ε  = β 1 + β 3 Z  = β 3  The coefficient (and standard error) on the interaction term tells us the direction, magnitude, and significance of the “interaction effect”.

40. Interaction Terms in Non-Linear Models: An Aside  Logit World  P(y i = 1) = = Λ(x i β) = Λ  = [Λ(1-Λ)][β 1 + β 3 Z]  = β 3 Λ(1-Λ) + (β 1 + β 3 Z)(β 2 + β 3 X)Λ(1-Λ)(1-2Λ)

41. Interaction Terms in Non-Linear Models: An Aside  Logit World  The coefficient (and standard error) on the interaction term does NOT tell us the direction, magnitude, or significance of the “interaction effect”.  The interaction effect depends on the values of all of the other variables.

42. Interaction Terms in Non-Linear Models: An Aside  P(y i = 1) = = Λ(x i β)  x i β = β 0 + β 1 X + β 2 Z + β 3 XZ  Let β 0 = β 1 = β 2 = β 3 = 1  A simulation…

44. RegressorModel 1 (random effects)Model 2 Ideological Incompatibility-0.007* (0.002) -0.005* (0.002) Polarization0.002 (0.004) -0.001 (0.02) Electoral Threshold0.026* (0.01) 0.021* (0.005) Polarization*Electoral Threshold0.0003 (0.0003) 0.0002 (0.0001) Coalition Size0.043* (0.01) 0.041* (0.008) Coalition Size 2 -0.0005* (0.0001) -0.0004* (0.0001) Asymmetry-0.144 (0.286) -0.01 (0.22) Asymmetry*Coalition Size-0.025* (0.008) -0.024* (0.006) Constant-2.46* (0.29) -2.10* (0.18) N Log Likelihood 3495 -613.49 3495 -663.95 Dependent Variable: Pre-Electoral Coalition (0,1) * p < 0.05 (two-tailed)

45. Quantities of Interest  Predicted probabilities  What’s the predicted probability that y = 1 (i.e., that a pre-electoral coalition forms)?  Note that we often report this for probit/logit models, but not when we use OLS…  Marginal effects  What’s the effect of a very, very small change in x on the probability that y = 1?  First differences  How does the probability that y = 1 change when we increase x by one unit (or some number of units)?

46. Effect of a One Unit Increase in Electoral Thresholds on the Probability of Electoral Coalition Formation Party System Polarization Effect of Electoral Thresholds 95% Confidence Intervals

47. Effect of a One Unit Increase in Party System Polarization on the Probability of Electoral Coalition Formation Effect of Party System Polarization Electoral Threshold 95% Confidence Intervals

48. Effect of a 0.01 Unit Increase in Asymmetry on the Probability of Electoral Coalition Formation Effect of Asymmetry Expected Coalition Size 95% Confidence Intervals

49. Effect of a One Unit Increase in Expected Coalition Size on the Probability of Electoral Coalition Formation (When Asymmetry is one standard deviation below its mean) Effect of Expected Coalition Size Expected Coalition Size 95% Confidence Intervals

50. Expected Coalition Size Effect of a One-Unit Increase in Expected Coalition Size Asymmetry is one standard deviation below its mean Asymmetry is at its mean Asymmetry is one standard deviation above its mean Shifts to the left as Asymmetry increases

51. Substantive Effect of Explanatory Variables on Electoral Coalition Formation Holding all other variables at their means

52. Example If all countries had the electoral threshold of Denmark in the 1970s (2%), and moved to the slightly higher threshold used by Norway in the 1970s (8.9%), the predicted probability of pre- electoral coalitions forming would jump by 181% and we would see an additional 59 electoral coalitions.

53. Conclusions

54. Summary: Before  Electoral coalitions are a simple function of electoral rules. “The more disproportional the electoral system, the greater the incentives for pre-electoral alliances”

55. Summary: After  Electoral rules do not have a direct unconditional effect on electoral coalition formation.  Pre-electoral coalitions are more likely when:  Potential coalition partners share similar ideological preferences.  Parties are of roughly equal size.  The coalition size is large, but not too large.  The party system is polarized and the disproportionality of the electoral rules creates an electoral bonus from forming a coalition.  Model explains cross-national variation and temporal variation within countries.

56. Why might you care about this?  Electoral coalitions offer the opportunity of combining the best aspects of the ‘majoritarian’ and ‘proportional’ visions of democracy.  We could increase the likelihood of electoral coalition formation by making electoral rules more disproportional.  The actual effect of changing the electoral rules will depend on the size and ideological polarization of the party system in each country.

57. Why might you care about this?  Electoral coalitions have an effect on various aspects of post-election government formation.  Governments based on electoral coalitions are more ideologically compatible than other governments and they form more quickly.  Electoral coalitions increase the likelihood that member parties enter government.  Differences between governments that form in the post-election versus inter-election periods.

58. The End