Coalition theories

1. Coalition theories From seats to government • After elections, parliamentary seats are assigned and parliamentary party groups formed • Then coalition bargaining – if necessary – begins for the formation of the government/executive (cabinet)

2. Parliamentary coalitions • Coalition theory tries to explain which government coalitions are more likely to be formed • Given the electoral results, what are the factors that are likely to determine the formation of certain coalitions? • These criteria are based on assumptions about party behaviour

3. Coalition theories: a map Minimal connected winning coalition (Axelrod) Minimum range (Leiserson) Office-seeking Policy seeking Cooperative Game Theory Minimal/minimum Winning coalition (Riker) Unidimensional De Swann Bargaining Proposition (Leiserson) Bidimensional Institutions free (Laver;Schofield) Bargaining theories (Baron, Diermeir,Merlo etc.) Non Cooperative Game Theory Institutional rich (Laver, Shepsle)

4. Cooperative and Non Cooperative Game Theory • Cooperative game theory investigates coalitional games with respect to the relative amounts of power held by various players, or how a successful coalition should divide its proceeds. • In contrast, noncooperative game theory is concerned with the analysis of strategic choices. The paradigm of noncooperative game theory is that the details of the ordering and timing of players’ choices are crucial to determining the outcome of a game. • In the cooperative games binding agreements are possible before the start of the game.

5. A coalition C is a sub-set non empty of a set N of all players • A cooperative game is given by specifying a value for every (nonempty) coalition. A so called characteristic function v assigns for each coalition a payment. The function describes how much collective payoff a set of players can gain by forming a coalition. The players are assumed to choose which coalitions to form, according to their estimate of the way the payment will be divided among coalition members. It is assumed that the empty coalition gains nil or in other terms v(Ø)=0. • v(TS)  v(S) + v(T) if S  T= Ø ; • An imputation is a game outcome (a possible solution) or a payoff distribution (x1, x2…xn) among n players that respects the following conditions: • iNxi = v(N); the players redistribute the “income” of the coalition • xi  v(i) for any player i ; None accepts a payoff inferior to what he/she could earn on his/her own Cooperative Game Theory

6. 5. An imputation x dominates an imputation y for a coalition C iff • The payoffs from x are higher than the payoffs from y for at least some member of C (and equal for the others) • The sum of the n members payoffs of the coalition C does not overcome v(C) • 6. Definition of Core: the set of non dominated imputations or the set of Pareto-optimal outcomes in a n-players bargaining game. • 7. A simple game is a special kind of cooperative game, where the payoffs are either 1 or 0. I.e. coalitions are either "winning" or "losing". In other terms if W is the subset of the winning coalitions, v(W) = 1. A winning coalition cannot become losing with the addition of new members • 8 A weighted majority game is a simple game in which a weight wi (for instance percentage of MP’s) is assigned to each player i and a coalition is winning when the sum of the w of each coalition member is superior to a level q (for instance 50% of the majority rule) . Formally iCwi q;

7. Office-seeking models In these models the political actors are motivated only by the interest for the advantages coming from the office. The coalition making is represented as a weighted majority game where the payoffs are either 1 or 0. As the payoffs are constant (1) and are not increased by adding new members to the coalition, winning coalitions with members non necessary to win give smaller portions of payoffs to its members than smaller coalitions without unnecessary members Winning coalition with 80% of seats Winning coalition with 58% of seats Bigger slices!! C:Seats 18% Po=0,225 C:Seats 18% Po=0,3103 B:seats 21% Po=0,3620 B:seats 21% Po=0,2625 D:seats 22% Po=0,275 A:seats 19% Po=0,3275 A:seats 19% Po=0,2375

8. Office-seeking models A winning coalition without unnecessary members is called “minimal winning coalition” The election of June 1952 in Netherlands Too many game solutions. Riker hypothesizes that out of the minimal winning coalitions it will form the coalition requiring as least resources (seats) as possible: the minimum winning coalition

9. Office-seeking models The election of June 1952 in Netherlands VVD:10 0,1754 VVD:10 0,1886 PvdA :33 0,5789 PvdA :33 0,6226 CHU:10 0,1886 ARP:14 0,2456

10. Office-seeking models According Leiserson among the minimal winning coalition the coalition with the smallest number of parties will form because of the bargaining costs The election of June 1952 in Netherlands

11. Office-seeking policy “informed” models According a pure office seeking coalition model policy positions does not matter and coalition among ideologically different parties are possible. However parties very different in terms of the ideology must pay very high bargaining costs. Axelrod: Minimal connected winning coalitions: The political actors can be ordered along one dimension . The minimal winning coalitions must have members ideologically adjacent. Leiserson: Minimum Range: the winning coalitions must minimize the ideological distance between the two extreme parties of the coalition.

12. Office-seeking policy “informed” models The election of June 1952 in Netherlands

13. In these models the political actors are motivated also by the policy distance between the expected policies of the government coalitions and their policy platforms. de Swann : Cooperative game-unidimensional. The policy positions are ordered along one dimension. A political actor will prefer the winning coalition whose policy position is the nearest to its preferred policy position. In only one dimension any winning coalitions (in a majority voting game) must include the party where is located the median voter. This party is called the Core Party, it cannot be excluded by the winning coalition and it controls its formation. The coalitions in the Core (or the winning coalitions) can be more than one. According that de Swann the Core Party should prefer the coalition that minimize the difference in terms of seats among the actors on the left and on the right of the Core Party in the coalition or in other terms the Core Party should prefer balanced coalitions. Policy-seeking models in one dimension

14. Core Party Policy-seeking models Seats=100 L (45) C (15) R (40) a) L (55) CL (20) CR (10) R (15) b) L (25) CL (15) C (8) CR (5) R (47) c) a) According to de Swann L,C,R is better for C than C,R or C,L as |45-40|<|0-40|<|0-45| b) Of course the best one is L c) L,CL,C,CR,R is better for CR as |48-47| < any other difference.

15. Policy-seeking models Seats=100 L (45) C (15) R (40) a) L (55) CL (20) CR (10) R (15) b) L (25) CL (15) C (8) CR (5) R (47) c) • Def. Pareto Set: the set of points in the policy space that: • For any point not in the set there is in the set a point that is preferred by all political actors taken in consideration. • Given a point in the set none else is considered better by all political actors • For any winning coalition the Pareto set is given by the line connecting the political actors members of the coalition

16. Policy-seeking models Seats=100 L (45) C (15) R (40) a) L (55) CL (20) CR (10) R (15) b) L (25) CL (15) C (8) CR (5) R (47) c) The Core Party is the party present in all Pareto Sets of all winning coalition. It always exists in a unidimensional world but..

17. Policy-seeking models in a bidimensional policy space (Schofield) A (20) Considering to simplify the analysis, only the minimal winning coalitions, in this policy space no Party is “member” of all Pareto Sets of all coalition. There is always a majority that can defeat any party platform. B (20) C (20) D (40)

18. A (20) In this situation there is a a party that is always included in all Pareto sets of all winning coalition. It is D. No majority can defeat the D’s political platform. B (20) D (40) C (20)

19. A (20) However usually a centrally located party is a Core Party if it is quite big.Otherwise no core party exists. C is not a Core party as is not in the Pareto Set of the coalitions AD and DB. Even when a small party centrally located is a Core party such a equilibrium is structurally unstable. …. B (20) C (20) D (40)

20. The election of June 1952 in Netherlands Traditionalism A structurally stable core at the KVP position ARP:14 KVP:33 CHU:10 PvdA:33 Left Right VVD:10 Modernization

21. The election of June 1952 in Netherlands Traditionalism A structurally stable core at the KVP position ARP:14 KVP:33 CHU:10 PvdA:33 Left Right VVD:10 Modernization

22. Traditionalism A structurally unstable core at the ARP position PvdA:33 ARP:14 VVD:10 CHU:10 Left Right KVP:33 Modernization

23. A structurally unstable core at the ARP position: after a small change in its policy position, ARP is not a Core Party any more as the Pareto set PdvA, KVP,VVD does not include it. Traditionalism PvdA:33 ARP:14 CHU:10 VVD:10 Left Right KVP:33 Modernization

24. However even if it does not exist a Core Party, the area of the disequilibrium is delimited by the intersections of the median lines. The so called Cycle Set. Core+Cycle set= Heart Traditionalism PvdA:33 median ARP:14 CHU:10 VVD:10 Left Right KVP:33 median Modernization median

25. Policy-seeking models in a bidimensional policy space (Laver-Shepsle) • Laver-Shepsle theory is a theory about government formation, is not a theory about “platform” bargaining. • Laver-Shepsle approach models a real decision making process, considers an initial status quo: it belongs to non cooperative game theory. R yes R Proposes x1 no x1 installed? P1 sel. x1 Vetoed? x1 new SQ R no yes Proposes x2 yes R R P2 sel x2 Vetoed? no x2 installed? no x2 new SQ R Proposes xi yes yes R R R Pi sel xi Vetoed? no xi installed? no xi new SQ Proposes xn R yes yes Pn sel xn Vetoed? R R no xn installed? xn new SQ R no yes

26. A government programmeof ideal policies According to Laver and Shepsle, the choice of government is not that of a generic policy programme, but that of a set of ideal policies of those parties that manage to allocate their own leaders to the different ministerial positions 26

27. Government formation is also an act of delegation from the parliamentary support coalition to the executive It is based on a trade-off of benefits (e.g. efficiency, expertise) and costs (e.g. risk of drift – ministerial drift) Government formation in parliamentary democracies 27

28. The set of possible governments Possible governments forms a discrete set of points on a multi-dimensional space Each government is characterized by a set of policies implemented by parties in charge of those specific policies ‘Being in charge’ of a policy means having a party representative heading the specific ministry 28

29. Example Three parties A, B and C Two key policies: economic policy and foreign policy No party has the majority, but any two parties do There are 32=9 possible governments that correspond to how the two positions (economic minister, foreign minister) can be allocated to the two parties Of these nine governments, 3 are single party and 6 are coalition governments 29

30. foreign policy forC forA forB AC BC CC AA CA BA AB BB CB ecoA ecoB ecoC economic policy The lattice of possible governments 30

31. A stable government Which of these governments is stable? Assume that the status quo government is BA, that is, the economic minister is from party B while the foreign minister is from party A (note that BA is different from AB even if the coalition is the same) Is there a majority coalition that prefers a government to BA among those possible? Is the majority winset of BA empty? 31

32. AC BC CC AA CA BA foreign policy AB BB CB economic policy Party A prefers governments inside the circle centered in AA and radius AA-BA to the government BA, and prefers government BA to those outside the circle. The same applies to the other parties 32

33. AC BC CC AA CA BA foreign policy AB BB CB economic policy W(BA) is empty BA is stable government 33

34. Defence spending dC dA dB AC BC CC AA CA BA AB BB CB sA sB sC Social spending Winset of BB B is a strong party 34

35. Where A and C can coalesce against B, there are only coalitions that include B • Hence B can decide not to join these coalitions as it prefers government BB • B is a strong party • If it exists, there is a single strong party • A strong party is member of any stable government coalition

36. Merely Strong Party: Although some legislative majority prefers at least one coalition government to the government in which a MSP gets all the portfolios, the MSP is a member of each of these alternative coalitions (B is a MSP) • Very Strong Party: A very strong party is a party to which a majority coalition prefers to give all the government portfolios rather than support any other government alternative.

37. AE BE CE DE EE CD DD BD AD Possible Minority government CC stable. C is a very strong party CC DC BC AC BB CB AB DB Warfae policy AA CA DA BA Welfare policy

38. CDU Foreign Policy FDP SPD G Taxation-spending German Elections 1987 CDU-FDP The W(CDU-FDP) is empty and CDU-FDP gov confirmed

39. CDU Foreign policy FDP SPD G Taxation - spending W(CDU) has only gov with CDU CDU is a strong party

40. Optimal government and the risk of ministerial drift 40

41. Control mechanisms in parliamentary governments Government formation is an act of delegation Parties may ex-ante negotiate the terms of the coalition (policy x) But the risk of ministerial drift remains CONTROL MECHANISMS: Government programs (credibility issue) Inter-ministerial committees Overlapping policy jurisdictions Undersecretaries Legislative review 41