Game Theory in the Study of Coalition Government

1. Game Theory in the Study of Coalition Government EITM-Harvard July 10, 2002 Daniel Diermeier Copyright 2002 D. Diermeier

2. Two Dogmas • Minimal Winning coalitions are the “natural outcome” of coalition bargaining; minority and supermajority governments need to be “explained” • reduced form analysis (regression/duration/etc.) is the right empirical methodology to study coalition government • Duration • Formation • Type Copyright 2002 D. Diermeier

3. Empirical Regularities • Minimal Winning Governments are not the norm (Strom 1990, Laver and Schofield 1990) • they occur in only 39% of cases where no party holds a majority of seats (36% overall) • Minority Governments are common (Strom 1990, Laver and Schofield 1990) • they occur in 37% of all cases where no party holds a majority of seats (33% overall) • In some countries they are the norm: of the 20 Danish governments between 1945 and 1987 19(!) were of the minority type Copyright 2002 D. Diermeier

4. Empirical Regularities – Cont’d • Minority Governments are less stable than other governments (e..g. Strom 1990), • but some minority governments last the entire term. • Moreover, if a minority government falls, it is frequently replaced by another minority government even after an early election. • Surplus majority governments are not rare (Laver and Schofield 1990) • 23% of all governments where no party holds a majority of seats are of this type (21% overall) • In Italy the percentages are 45% and 40% respectively Copyright 2002 D. Diermeier

5. Previous Work • There is no theoretical approach that can account for these facts simultaneously • Strom (1990) suggests two reasons for minority governments: • electoral costs of being in the government (“incumbency disadvantage”) • influence on policy by opposition parties through other means, e.g. strong committees • but empirical evidence is shaky for both factors • lack of evidence for incumbency disadvantage (Stevenson1997) • strong committees are not sufficient (Germany has some of the strongest committees in parliamentary democracies (Lees and Shaw 1978), but never had a minority government at the federal level). • Laver and Shepsle (1990) suggest a structure-induced equilibrium model for minority governments, but Austen-Smith and Banks (1990) show that their results are not robust. • Baron (1998) shows that minority governments can be stable, but that they are never chosen in equilibrium. Copyright 2002 D. Diermeier

6. Basic Idea • Basic idea: • Interpret cabinets as the outcome of a bargaining process between disciplined parties (like Lupia and Strom (1995) and Diermeier and Stevenson (1998)). • Use a dynamic model with both policy and electoral (opinion) shocks • Hence dynamic concerns will drive government selection: type and duration of government are selected simultaneously in equilibrium • Two-period spatial model of government formation and termination (with common discount factor ) Copyright 2002 D. Diermeier

7. Preferences • Three parties; no party has a majority of seats;  is the vector of seat shares. • Parties have: • (quadratic) preferences over policy (in 2) • (linear) preferences over distributive benefits (jobs for party members, etc.) • quasi-linear per-period pay-off • Parties’ ideal points are located on equilateral triangle. • default policy q{z1,z2,z3};if q=zi , i is called the “favored party”. Copyright 2002 D. Diermeier

8. Proto- Coalition Bargaining • Using Baron and Diermeier (1998) we assume that proto-coalitions bargain efficiently over policy and allocation of benefits. • For each proto-coalition D and default policy q this allows us to: • identify the chosen policy (D’s centroid). • define a “cake”, that is a measure (in aggregate) benefits of how much the proto-coalition D would be better off in forming the government policy rather than staying with the default policy. • Proto-coalitions bargain (over the cake) according to a Rubinstein-Binmore et al.-Merlo&Wilson bargaining model: • each party is selected to make a proposal (a benefits/policy proposal) with probability 1/|D| until all members of the proto-coalition agree. • if the members cannot agree, the default policy is implemented, no transfers are made and a new proto-coalition is selected. • in equilibrium members share the cake equally; this allows us to calculate transfers for every party in D. Copyright 2002 D. Diermeier

9. From Proto-Coalitions to Coalitions • If there is a government in place it constitutes the proto-coalition; if not a formateur is selected proportional to seat share by the head of state (Diermeier and Merlo 1999). • Proto-coalitions are not restricted to be minimal winning; they may also be of the minority or supermajority type. • Proto-coalitions need to obtain the confidence of the chamber • to do so, they can allocate benefit transfers to each party outside the coalition. • this will be irrelevant if the proto-coalition commands a chamber majority, but crucial to minority governments. • if the proto-coalition fails to obtain the confidence of the chamber, the default policy is implemented. • This implies the following notion of government: • a government is identified with an allocation of cabinet portfolios. • a party that supports a minority government on critical votes is not part of the government. • members of the government jointly decide on policies and allocations of government posts. Perks can be transferred to outside parties. Copyright 2002 D. Diermeier

10. Time Line • Period 1 • Given: seat shares  and default policy q • Since no government is in place, the head of state chooses a formateur party proportional to seat share • Formateur selects proto-coalition and possibly transfers to outside parties subject to chamber confidence • Proto-coalition bargaining on policy and benefits • If formateur proposal or proto-coalition fails, q is implemented Copyright 2002 D. Diermeier

11. Time Line – Cont’d • Period 2 • Given: current seat shares , new default policy q’ with probability , new seat shares (if early election was held) of ’=  +  (where  is “small” random vector with mean (0,0,0) subject to some technical conditions) • Incumbent government can “renegotiate” its policy and transfers (within coalition and to outside parties) subject to majority approval; this is similar to proto-coalition bargaining with the incumbent government as the proto-coalition • If government fails to reach agreement or looses confidence, it terminates; in this case the chamber decides on whether to call an early election • If an early election is called government formation proceeds as in period 1 but with ’ as relevant seat share; otherwise the old seat share  is used. Copyright 2002 D. Diermeier

12. Results - Part One • Last Period Government Formation • if D is chosen as proto-coalition it chooses centroid for any q all proposed coalitions are accepted • no government makes any transfers to outside parties (including minority governments) • a minimum winning coalition never forms (!) • if the favored party is chosen as a proposer it forms a super-majority government; any non-favored party chooses a minority government. • Dissolution versus Replacement • whenever ’ an early election is called • We can then calculate each party’s expected pay-off if the incumbent government terminates; this defines outside options for the renegotiation process. Copyright 2002 D. Diermeier

13. Results - Part Two • Renegotiation • Majority governments never terminate, but they have to reshuffle transfers if the default policy changes. • Minority governments may terminate depending on seat shares ’ (or ) • Why? In contrast to the last period case minority governments now need to make transfers to at least one outside party; this follows because if the minority government falls, an opposition party may be chosen proportional to its relative seat share. This defines an outside option for the opposition parties for which they must be compensated by the minority government. If the price is too high (that is, higher than the minority party’s outside option), the minority government terminates. • Note: if we restrict attention to majority governments (like Lupia and Strom) then governments never terminate. This suggests that their results are not robust once we allow for renegotiation. • As before this allows us to calculate each party’s expected pay-off for coalition formation in period one. Note that for majority governments this only depends on nature of reshuffle, while minority governments need also to include the risk of terminating. Copyright 2002 D. Diermeier

14. Results - Part Three • First Period Government Formation • All types of governments may be chosen in equilibrium • Minority government may be chosen even though each party expects that they may not last the entire term • In contrast to the one-period case, minimum winning coalition may form. Why? • favored parties would consider to form super-majority governments, but need to compensate only one other party in the renegotiation stage if they propose minimum winning coalition instead • non-favored parties would consider to form minority governments with outside support (of e.g. party k); however, in the next period they would likely seek the support of party j; for that risk it has to compensate party k; this may make it cheaper to form a minimal winning government in the first place. • This provides a new and radically different justification for minimal winning governments (compared to Riker 1962 and Baron 1989) that crucially depends on the possibility of renegotiation in future periods. Copyright 2002 D. Diermeier

15. Figure 1 Coalition formation if the formateur is the favored party 2 1/2 {1,3} (1+)/6  {1,2,3} {1,2} 3 0 (1+)/6  1/2 In this example party 1 is the formateur, q=z1, and  = 1. The area where {1,2,3} is chosen increases as  decreases until at =1/2 it covers the entire upper triangle (i.e. the parameter space )

16. Figure 2 Coalition formation if the formateur is not the favored party 1 1/2 {2}*  1=2(1-3)/5 {2}** {2,3} 3 0 1/2 In this example party 2 is the formateur, q=z1, and =1; in the region indicated by * {2} always survives in period 2, while in the region indicated by ** {2} terminates with probability (1-)/2.

17. Summary and Outlook • We provided a model that can explain the following empirical phenomena: • All types of government can occur (minimal winning, minority, surplus) • Minority Governments are less stable than other governments, but some minority governments last the entire term. • If a minority government falls, it is frequently replaced by another minority government even after an early election. • The model does not have any of the theoretical problems of Lupia and Strom • it is dynamic and stochastic • it allows for renegotiation • it does not rely on transaction costs Copyright 2002 D. Diermeier

18. Summary and Outlook – Cont’d • The analysis gives an new explanation for why different types of governments occur. It suggests that the right question is not “Why do minority and surplus governments occur?”, but rather “Why don’t they always occur?” The answer is the threat of termination and renegotiation. • What’s next? • extend to multi-period case to establish tight connection to government survival literature • vary institutional features of government selection and termination to investigate cross-country differences (e.g. constructive vote of confidence) • empirical analysis using structural estimation Copyright 2002 D. Diermeier

19. Analyzing Parliamentary Constitutions • Different constitutional rules for government formation and termination • Different outcomes: • duration of government formation • government composition • government stability • Key Questions: • Do constitutional differences matter ? • How much? Copyright 2002 D. Diermeier

20. The Research Agenda • Conduct experiments of comparative constitutional design • Evaluate effect of (DEM 2000): • Investiture requirement • Constructive vote of no-confidence • Fixed inter-election period • Evaluate effect of (DEM 2001): • Bicameralism Copyright 2002 D. Diermeier

21. Methodology • Propose game-theoretic model of government formation • Estimate structural parameters • Conduct constitutional experiments Copyright 2002 D. Diermeier

22. The Application-Bicameralism • While recognized as important by constitutional designers (“Federalist Papers”!!), not widely studied • Existing political economy literature: • Diermeier and Myerson (1999) • Effect on internal organization of legislatures • Tsebelis and Money (1997) • Effect of second chamber and inter-chamber bargaining institutions on legislative output • Focus on legislative bicameralism • Today: governmental bicameralism Copyright 2002 D. Diermeier

23. Dual Responsibility • In some countries a government must maintain confidence in two chambers (Italy, Sweden until 1970, Belgium until 1995) • This may (?) suggest: • shorter government duration • more frequent surplus or oversized governments Copyright 2002 D. Diermeier

24. Two Conjectures • Tsebelis (2000): • (1) Bicameralism leads to shorter government duration • Lijphart (1984), Sjölin (1993): • (2) Bicameralism encourages oversized coalitions Copyright 2002 D. Diermeier

25. Existing Literature • Druckman and Thies (2001) • Regression approach (Cox-Proportional Hazard) • Support for (1) (duration effect) • No support for (2) (formation effect) • But: only consider governing coalitions that lack majority status in upper chamber • Confounding legislative and governmental bicameralism • No work on dual responsibility ! Copyright 2002 D. Diermeier

26. Our Goal • Use structural model to assess effect of dual responsibility • Estimate structural model for Belgium • Conduct “counterfactual” constitutional experiments to assess qualitative and quantitative effects of eliminating dual responsibility. • Compare outcome with “real” reform conducted in Sweden. • Note: not a “natural experiment”! Copyright 2002 D. Diermeier

27. Methodology • Explicitly incorporate the main features of an institutions into the structure of the model • Holding the institutional structure constant, use data to obtain estimates of the fundamental parameters of the model • Use simulation methods to investigate the effects of changes in the institutional structure (“counterfactual” constitutional experiments) in the context of the estimated model Copyright 2002 D. Diermeier

28. Advantages over Traditional Methods • The results obtained can be interpreted as equilibrium phenomena • Changes in constitutional features lead to equilibrium responses by strategic actors • The estimates obtained can be used to conduct counterfactual constitutional experiments with fully strategic actors • To the extent that institutional features can be directly incorporated into the model’s structure, the number of parameters that need to be estimated does not necessarily increase with the richness of the institutional environment Copyright 2002 D. Diermeier

29. Example • Three parties {1,2,3}; party 1 is proposer; 5 periods • H=(1/5,1/5,3/5), S=(1/5,3/5,1/5) • Dual Responsibility: • Minority:{1} duration: 1 (bad), 2 (good) • Partial: {1,2} and {1,3} duration: 2 (bad), 3 (good) • Surplus:{1,2,3} duration: 3 (bad), 4 (good) • Single Responsibility: • Minority:{1}, {1,2} duration: 2 (bad), 3 (good) • Minimal:{1,3} duration: 3 (bad), 4 (good) • Surplus:{1,2,3} duration: 3 (bad), 4 (good) • Taste: 1{1}= 1{1,2}=1/2, 1{1,3}= 1{1,2,3}=0 • Bargaining protocol: if 1 is not accepted, pi=1/|D|. Copyright 2002 D. Diermeier

35. Key Features of the Model • Equilibrium selection of coalitions depends on constitutional features • Fundamental trade-off between “durability” (larger coalitions are more durable and hence produce a larger “cake”) and “control” (larger coalitions imply smaller pieces of the “cake” for each coalition member) • Shorter expected proto-coalition duration (type-by-type) will lead to equilibrium replacement effect • Effect on duration is ambiguous Copyright 2002 D. Diermeier

36. “Counterfactual” Experiment • Suppose in 1946 Belgium had eliminated government responsibility to the Senate. • What would have been the effects according to our model? Copyright 2002 D. Diermeier

37. Belgium-Results standard errors in parentheses Copyright 2002 D. Diermeier

38. Belgium Predictions standard errors in parentheses Copyright 2002 D. Diermeier

39. “Real” Experiment (Sweden) • In 1970 Sweden abolished its First Chamber (its “Senate”). • What were the effects? Copyright 2002 D. Diermeier

40. Sweden - Outcome Copyright 2002 D. Diermeier

41. Main Results • Eliminating government responsibility to the second chamber • does not increase government stability • does produce smaller government coalitions • main shift is from majority to minority governments (“over-shooting”) • Main theoretical reason: equilibrium replacement due to strategic selection by formateur Copyright 2002 D. Diermeier