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Coalition Theory and Government Formation

Abstract and Keywords

This article tries to show how bargaining theory has helped people understand key aspects of government formation. It also shows how people's understanding of coalition bargaining has slowly moved past the simplistic assumptions of the first generations of such theories. The article examines three specific questions in detail, and then considers the factors that influence whether specific parties or types of parties obtain government membership.

Keywords: bargaining theory, government formation, coalition bargaining, government membership, coalition theory

1 Coalition Bargaining, Government Formation, and Representative Democracy

A coalition is a team of individuals or groups that unites for a common purpose. For example, teams of politicians, who may all belong to one or several political parties, coalesce for the purpose of running a government. Together, these coalition members convert a wide range of social demands into a manageable set of public policies. This is only one form that coalition politics takes, but in democratic societies it is probably the most important one.

The ability of political actors to form successful coalitions is essential to representative democracy. In a democracy, no one person can legislate or exert power without (p. 783) the support of others. Open societies typically foster a multitude of political actors who must join forces to have any hope of getting their way. Democratic rules generally require that decisions be supported by a simple or qualified majority of the people's elected representatives.

While working for a common cause, coalition members may disagree about important matters. Some disagreements stem from attempts to please distinct constituencies. For example, members who represent urbanites want policies that are different from those favored by representatives from rural regions. Conflicts can also arise when multiple members compete for important and scarce spoils or offices (e.g. that of the prime minister). How coalition members pursue their common interests and manage internal conflicts affects the fate and effectiveness of the coalitions they form.

Understanding coalition bargaining helps us grasp not only government decisions, but also who gets into government in the first place. This is particularly true in parliamentary democracies, where the government (executive) rests on the support of the parliament. Although coalition bargaining among political parties in presidential democracies can be quite important (Amorim Neto 2006; Cheibub 2002; Cheibub, Przeworski, and Saiegh 2004), it generally does not as directly affect who controls the top executive offices. Hence, the primary focus of this chapter is on government formation in parliamentary democracies.

In parliamentary regimes, government coalitions are typically formed by and through political parties. Political parties are in themselves coalitions of individual politicians who run for election under the same label. In bargaining over control of the government, however, parties tend to behave very cohesively. Hence, this chapter follows the bulk of the literature on government formation, focusing on coalition bargaining amongst unitary political parties (see Laver and Schofield 1990; Müller and Strøm 1999 for justifications of the unitary party assumption).1 Party cohesion in parliamentary systems is driven in part precisely by the government's need to maintain parliamentary support (or at least toleration) at all times. In presidential systems, the executive is not so vulnerable, and consequently party cohesion also tends to be lower.

At every stage of a government's life cycle in parliamentary democracies, coalition decisions emerge from bargaining. Parties to such bargains have to be backward looking and forward looking at the same time. The outcomes are shaped not only by past bargains that affect the members' resources and the constraints under which they operate, but also by the fact that bargaining occurs in the shadow of future elections and under the constant threat posed by political rivals.

Bargaining theory, and more generally the game‐theoretic tradition, has since Riker's (1962) seminal work been the dominant analytical framework in which coalition formation has been understood. In this chapter we show how bargaining theory has helped us understand key aspects of government formation, but also how our understanding of (p. 784) coalition bargaining has gradually moved beyond the simplistic assumptions of the first generations of such theories. We examine three specific questions in more detail: First, under what circumstances do coalition governments form? Second, what accounts for the type of government that forms? In other words, what determines whether the emerging government has minority support in parliament, whether it is a minimal winning coalition, or whether it is a surplus coalition? Finally, we consider the factors that influence whether specific parties or types of parties obtain government membership.

2 Stable or Ad Hoc Coalitions?

The most fundamental question about coalition formation is one that is rarely raised. Coalitions can be made one issue or bill at a time, or they can be (by intention, at least) much more durable and comprehensive. What explains the choice of ad hoc versus stable coalitions? To the extent that political parties are a stable coalition of politicians, this is a question that we can drive all the way down to the level of the individual legislator. Why might politicians prefer to operate as solitary and sovereign decision makers, choosing sides from issue to issue with whatever allies might be available? And, on the other hand, why do politicians sometimes (in fact, often) submit to party authority and decide to support the policies and alliances that their party leaders favor? Similarly, the parties to which these politicians belong can form either ad hoc, free‐floating coalitions, or more stable, formalized ones.

These decisions can best be understood within the framework of transaction cost politics (Dixit 1996; Strøm, Müller, and Bergman 2007). Free‐floating coalitions have their advantages. They allow for more freedom, and they are more efficient in the sense that parties or legislators never have to vote for proposals they do not sincerely favor. Nor do they have to pre‐commit themselves to common positions on issues that they may not even be able to anticipate. But on the other hand, compared to more stable or formalized coalitions, short‐term ad hoc alliances entail a range of disadvantages, such as:

  • Increased transaction costs. Free‐floating majorities force participants to negotiate every decision anew. The time and energy needed to proceed in this manner can exhaust a party's resources and reduce its abilities to accomplish broad or multiple goals. An important part of the rationale for stable coalitions is thus that they economize on transaction costs.

  • Less policy impact and continuity. Without a formal coalition, political decisions might not last long enough to be implemented, much less have any significant impact. In a setting without stable parties or coalitions, legislative victories may be very short‐lived. Why should the majority that forms on a Tuesday morning not overturn the laws made by Monday evening's rulers? Such instability would greatly reduce the value of any decision that a governing coalition would be able to make. (p. 785) After all, what is the value of governing if you have no idea whether your decisions will immediately be reversed? Such uncertainty adds another type of transaction cost.

  • Less faithful implementation. Even if a free‐floating majority were in power long enough to name its cabinet ministers, and even if its decisions were not immediately reversed, there is little reason to expect others in government to abide by these directives. Indeed, we should expect bureaucrats who dislike today's ministerial directives to disregard them if they believe that they can get away with it (see e.g. Huber 1998; Huber and Lupia 2001). In other words, just as on the high seas, the prospect of leadership instability makes mutiny more attractive.

  • Less policy credibility. The problem of policy credibility does not end with policy implementation. For most government policies to be effective, even people outside of government must cooperate. Citizens must abide by the laws, businesses must adhere to the terms of their contracts, and countries must act within the terms of their treaties. If a government cannot credibly uphold agreements tomorrow that its leaders sign today, anyone who deals with that government has less incentive to trust or cooperate with it. In a polity governed strictly by free‐floating majorities, public policy might have little long‐term credibility. This might adversely affect citizens in many ways. Imagine, for example, what buying a house or investing in stocks would be like if basic property rights were subject to frequent and unpredictable change. Indeed, people attempting to base important social, political, or economic plans on government policies would likely consider free‐floating majorities disastrous. Such lack of predictability could in turn cause economic inefficiencies and major social problems.

  • Less reliable voter support. In democratic countries, politicians can bargain for a place in government only if citizens delegate policy‐making authority to them through elections. The electoral connection—the threat that eventually voters will judge coalition members—governs their behavior. Therefore, if voters prefer a government whose actions are at least somewhat predictable, then politicians who can credibly commit themselves to something other than a transitory coalition stand to gain. Members of stable coalitions can also more easily establish “policy brand names” that reduce citizens' uncertainty about the policy consequences of voting for a particular candidate (Cox and McCubbins 1993). Indeed, stable coalitions make it easier for voters to hold government officials accountable for their actions than do free‐floating majorities.

In sum, formalized, stable coalescence is a survival strategy—it enables politicians to influence government decisions, earn the trust of non‐governmental actors, and maintain good long‐term relations with voters while paying relatively low transaction costs. For politicians operating in parliamentary institutions, they are a collective good. To the extent that such relations and cost savings are more important than the policy freedom that free‐floating coalitions could allow, stable coalitions should form.

Yet, politicians do not always choose stable coalitions. In some political systems, such as the Scandinavian countries, an environment of high information certainty and relatively low risks may be responsible for the fact that many parliamentary decisions are made through ad hoc or short‐term bargaining. In presidential democracies, parties (p. 786) are typically less cohesive, and decision‐making coalitions may often be more ad hoc (Cheibub, Przeworski, and Saiegh 2004). And in general, the fact that there may be collective benefits to be had from stable coalitions does not necessarily mean that legislators will choose to form them. Yet, even in situations in which formal executive coalitions do not form, stable legislative coalitions frequently exist (see e.g. Warwick 1994; Bale and Dann 2002). Thus, the absence of formal executive coalitions, in addition to being driven by transaction costs, also is influenced by the relative costs and benefits potential support parties can procure outside of government, particularly their ability to extract policy concessions without incurring the potentially high electoral costs of government membership (Strøm 1984, 1990b; Laver and Shepsle 1996; Mitchell and Nyblade 2006).

3 Government Type

Extreme turnover in cabinet offices is rare, although extreme stability is not the mode, either. In presidential democracies, executive terms are fixed (barring resignation, death, or impeachment), and this rigidity or predictability affects cabinet composition as well. Yet, the partisan composition of presidential cabinets may be more fluid than what is typical in parliamentary systems, since presidents may reshuffle their cabinets to increase their legislative or popular support. And in doing so, presidents will tend to be less constrained by the partisan composition of their cabinet (Amorim Neto 2006).

Given that government coalitions in parliamentary democracies tend to be fairly stable, the overriding concern among students of such governments has been to understand the type of coalition that forms. Scholars have found it useful to distinguish between governments based on the parliamentary support of the parties that participate in the government: whether these have minority support, constitute a minimal winning coalition, or have surplus members. Sometimes a single party may have a majority of seats and thus is able to govern alone. However, most parliamentary democracies, especially in Europe, feature proportional representation, which most often results in situations in which no party has a legislative majority. In such minority situations, it has traditionally been assumed that a majority coalition should form and that minority governments are deviations to be explained. This is because in parliamentary systems governments rest on the support—implicit or explicit—of a parliamentary majority (Müller, Bergman, and Strøm 2003).

Riker's influential work (see below) narrowed this prediction down to a minimal winning coalition. When a valuable prize is divided by a group, and the decision must be made by a simple majority rule, a minimal winning coalition maximizes the potential payoff to a majority of the group (Riker 1962). As government membership is generally considered to be a valuable prize, minimal winning coalitions should be favored.

(p. 787)

Although minimal winning coalitions may be the “natural” outcome of bargaining, they are in fact not the most common outcome, at least in minority situations in Europe. In Table 32.1 we report some basic characteristics of coalition governments in the context where they have most often been studied: national governments in the parliamentary systems of Europe. The table reports on a sample of 424 governments formed in seventeen West European parliamentary or semi‐presidential democracies from 1945 to 2000. Of these governments, only 13 percent were single‐party majority governments. Twenty‐two percent were single‐party minority governments, while 44 percent were majority and 18 percent minority coalitions. Out of the majority coalitions, roughly three‐fifths were minimal winning, whereas the rest were oversized. Thus, if we confine ourselves to minority situations, roughly 25 percent of the cabinets formed were single‐ party minority governments rather than formal governmental coalitions.2 Almost as (p. 788) many coalitions deviated from our expectation by being oversized. In minority situations, then, minority governments have been the modal category, followed by minimal winning coalitions and then by surplus governments. Most countries in Western Europe have experience with all three types of government, although there is wide cross‐national variation in the incidence of the various cabinet types.

Table 32.1 Coalition governments in Western Europe, 1945–1999

Country

Non‐ partisan

One party majority

One party minority

Coalitions

MWC

Surplus majority

Minority

n

n

%

n

%

n

%

n

%

n

%

n

%

n

%

Austria

22

0

4

18.2

1

4.5

17

77.3

14

63.6

3

13.6

1

4.5

Belgium

33

0

3

9.1

2

6.1

28

84.8

14

42.4

12

36.4

4

12.1

Denmark

31

0

0

14

45.2

17

54.8

4

12.9

0

27

87.1

Finland

44

7

15.9

0

4

9.1

33

75.0

7

15.9

20

45.5

10

22.7

France

23

0

1

4.3

5

21.7

17

73.9

7

30.4

8

34.8

7

30.4

Germany

26

0

1

3.8

3

11.5

22

84.6

17

65.4

5

19.2

3

11.5

Greece

11

1

9.1

7

63.6

1

9.1

2

18.2

1

9.1

1

9.1

1

9.1

Iceland

26

0

0

4

15.4

22

84.6

17

65.4

4

15.4

5

19.2

Ireland

22

0

6

27.3

6

27.3

10

45.5

5

22.7

0

11

50.0

Italy

51

1

2.0

0

14

27.5

36

70.6

4

7.8

23

45.1

23

45.1

Luxembourg

16

0

0

0

16

100.0

15

93.8

1

6.3

0

Netherlands

23

0

0

0

23

100.0

9

39.1

11

47.8

3

13.6

Norway

26

0

6

23.1

12

46.2

8

30.8

3

11.5

0

17

65.4

Portugal

14

3

21.4

2

14.3

3

21.4

6

42.9

3

21.4

3

21.4

3

21.4

Spain

10

2

20.0

2

20.0

6

60.0

0

0

0

6

60.0

Sweden

26

0

2

7.7

17

65.4

7

26.9

5

19.2

0

19

73.1

Britain

20

0

19

95.0

1

5.0

0

0

0

1

5.0

Overall

424

14

3.3

53

12.8

93

21.9

264

62.3

125

29.5

91

21.5

141

33.3

Source: Mitchell and Nyblade 2006.

4 Bargaining Theory and Government Formation

In order to make sense of these facts, let us consider the contributions of bargaining theory. The classic application of bargaining theory to political coalitions is William Riker's (1962) The Theory of Political Coalitions. Applying the logic of von Neumann and Morgenstern (1944) to political situations, Riker's most famous result—his “size prin‐ ciple”—predicts the formation of minimal winning coalitions. Using cooperative game theory, Riker modeled the formation of political coalitions as a fixed‐sum bargaining game, in which participants must agree to the division of something valuable to each of them (in our case, government membership). And as Riker succinctly suggests: “In social situations similar to n‐person, zero‐sum games, with side‐payments, participants create coalitions just as large as they believe will ensure winning and no larger” (Riker 1962, 47).

The size principle rests fundamentally on two further principles, which Riker calls the “strategic principle” and the “disequilibrium principle.” Undersize ruling coalitions will have incentive to add members because the majority of parliament that is excluded from government would have both the means and incentive to upset the minority government (the strategic principle). On the other hand, members of oversized coalitions will find that the benefits of government membership are being distributed too thinly and choose to eject surplus members of the coalition (the disequilibrium principle).

Of course, coalition formation is not always strategically identical to an n‐person, fixed‐sum game with side payments. The degree to which coalition formation in the real world approximates Riker's model clearly varies from case to case. The greater the divergence, the less explanatory or predictive power the model may have. While reality may diverge from Riker's model in numerous ways, several are of particular interest: the payoffs, the information available to the players, and the bargaining environment in which they operate.

4.1 Payoffs

Riker assumes that the payoffs from coalition bargaining are fixed sum, which means that one player's gain must be another player's loss, and that coalition members always receive a positive payoff and non‐members none. These assumptions are not always self‐evident. (p. 789) In the real world, parties sometimes turn down the opportunity to be a government member (e.g. the Agrarians in Sweden in 1957, the Christian People's Party in Norway in 1981, the Labour Party in Ireland on a number of occasions, see also Bale and Dann 2002), which should not occur if parties invariably derive positive utility from government membership and none from opposition. One reason why government membership may in fact be costly is that, at least in West European parliamentary democracies, government membership is more of an electoral liability than an asset (Rose and Mackie 1983; Narud and Valen 2006). Small parties that are particularly vulnerable in the electorate may have to think carefully about whether being a minor cog in a government coalition will be worth the likely electoral cost. Furthermore, it is worth the noting that the fixed‐sum payoff also is violated by the fact that the durability of the government varies with the type of government formed. Majority governments, for example, generally endure longer than minority governments. So not only does the size of the shares of power depend on coalition bargaining, so too may the value of the pie that is being divided, thus further complicating the bargaining situation (see Diermeier, Eraslan, and Merlo 2002, 2003).

If the value of incumbency varies, we should expect that the more “valuable” government is, the more likely MWCs will form. This is in fact the primary force driving Riker's size principle. What could make office more or less valuable? Three such factors suggest themselves: (1) the richness of the spoils of office, (2) the policy‐making opportunities that holding office entails, and (3) the expected electoral gains (or losses) resulting from incumbency (Strøm 1990b; Müller and Strøm 1999). On each of these dimensions, the value of office should be considered relative to the prospect of being in opposition (see Strøm 1990a, 42). Membership in a governing coalition is more valuable the greater the “perks” associated with it, the more it tends to positively influence electoral performance, and the more it moves policy outcomes closer to the preferences of its members (Müller and Strøm 1999). Thus, Strøm (1984, 1990a) considers two primary factors in explaining minority governments: electoral consequences and policy influence. The less governing parties are favored over the opposition in policy influence and expected electoral returns, the less attractive it is to be an incumbent, and the greater the likelihood of minority governments.

Existing scholarship has focused heavily on the second of these considerations, namely policy influence. Axelrod (1970) and De Swaan (1973) were the first scholars to give policy a more central role in the study of coalition bargaining. De Swaan assumed that policy coherence is the attribute actors attempt to maximize. Utility requires producing agreement on preferred policies and maintaining coalition harmony over time. Therefore, players prefer to join winning coalitions with the smallest possible dispersion in policy preferences (“closed minimal range” theory).3 The general behavioral assumption is that ideologically connected coalitions will have a lower conflict of interest and a therefore a greater policy value to their members. They should therefore also be easier to form and sustain.

(p. 790)

In recent work, most scholars have tended to move beyond the simple generalized office payoffs of Riker (1962) and Leiserson (1966), following Axelrod (1970) and de Swaan (1973) in incorporating parties' preferences over policy matters in modeling the bargaining game. These scholars frequently draw on the spatial bargaining logic of Black (1958) and Downs (1957), to emphasize the advantages of centrally located policy preferences, in unidimensional or multidimensional issue spaces (see Schofield 1993; Crombez 1996; Laver and Shepsle 1990, 1996).

These models emphasize how both relative size and central policy preferences enhance parties' bargaining power. Unlike extensions of Riker's approach, which generally explain coalition formation by focusing on the degree to which the bargaining situation conforms to their models, these models explain coalition types by focusing on the resources (seat shares) and preferences of those bargaining. Whereas these models differ in their relative emphasis on policy vs. office preferences, fundamentally they emphasize how differences in bargaining power, rather than differences in the bargaining environment, influence coalition formation.

The logic behind these bargaining power models is relatively straightforward, although in actual development they can become quite complex, as the models seek to incorporate multiple issue dimensions along with seat shares and sometimes other factors. Consider for the moment majority situations, in which, assuming that a simple majority is sufficient for winning, a single party is able to form a government by itself. While majority situations are generally ignored in most studies of government formation, they are instructive because they constitute the extreme case in which bargaining power is disproportionately concentrated in the hands of a single party. In a majority situation, by definition the majority party can form a minimum winning coalition, and it is also the median party on every issue dimension, which gives it disproportionate advantages in resource as well as office terms.

Yet, even in non‐majority situations certain parties may have disproportionate bargaining power. A large, centrally located party with many potential coalition partners may be in a position to form a government on its own. In general, the costs of not coalescing can in these cases be minimized. In non‐majority situations, the greater the bargaining power of the dominant player in coalition bargaining, the smaller the government is likely to be. That is to say, the concentration of bargaining power makes minority government more likely relative to MWCs and even more so relative to surplus coalition governments. This fundamental idea underlies the logic of almost all policy/size theories of coalition formation, and is most directly suggested by Crombez (1996) and Laver and Shepsle (1996).

Thus, the more bargaining power is concentrated in the hands of a single party, the less likely a coalition is to form. For example, this means that a near‐majority party is more likely to form a minority government, as it only needs to pick up a few seats for each parliamentary vote. Similarly, a single party that can consistently rely on parliamentary support from allies who are not in government improves its bargaining position compared to parties that do not have any allies of this kind. Generally, large parties that are centrally located have greater bargaining power, as they have the ability to form coalitions with parties that are both on their left and their right (Laver and Schofield (p. 791) 1990; Crombez 1996; Laver and Shepsle 1996). In presidential systems, and especially under divided government, bargaining power may tend to be more dispersed than under parliamentary government.

4.2 Information

Riker recognized that other assumptions of his model may be even less applicable to the real world. Perhaps most important is the assumption of complete and perfect information. Real‐world governments emerge from bargaining encounters in which the parties typically have much less than full information about their rivals' true preferences, what the next election may bring, and a range of other matters. The fewer and more cohesive the parties, and the longer and more consistent their track records, the more coalition bargaining situations are likely to approximate this rather stringent requirement. As the information of the players gets worse, they get more likely to hedge their bets by increasing the size of their coalitions. As Riker (1962, 88–9) suggests: “The greater the degree of imperfection or incompleteness of information, the larger will be the coalitions that coalition‐makers seek to form and the more frequently will winning coalitions actually formed be greater than minimum size.” Dodd (1976) tested this proposition on a sample of national governments and found supportive results.

The parties can attempt to reduce uncertainty by making credible commitments about their future actions. However, when the ability to make such credible commitments is absent or imperfect, coalition parties may have incentives to “blackmail” each other, threatening to bring down the government in order to extract concessions. To avoid this threat, a coalition may seek to add surplus actors as “insurance.” In a formal model of legislative coalition formation, Carrubba and Volden (2000) predict that in order to create a more stable logroll (and avoid “blackmail” by individual members), parties create “minimum necessary coalitions,” which may be larger than minimal winning. In a subsequent (2004) article, they suggest that surplus coalitions are particularly likely when the number of and diversity of actors is great, when bills are hard to pass, and when legislation tends to be costly or not very beneficial to its members. Operationally, they identify these conditions with a great number of parties and members of parliament, a bicameral system with the upper and lower house divided, a highly polarized parliament, and a small government (in the proportion of taxes relative to GDP).

In a series of publications in the mid‐1980s, Eric Browne and associates (Browne, Frendreis, and Gleiber 1984, 1986) presented a more radical critique of existing coalition theory, emphasizing the importance of unforeseeable events in coalition politics. Changes of government, they claimed, could best be understood not as resulting from informed and rational bargaining among party leaders, but as the consequences of random “critical events,” or exogenous shocks, that impacted on them. While few scholars have signed on to the full implications of this argument, subsequent scholarship has attempted empirically to incorporate exogenous shocks into models of cabinet duration (King et al. 1990) and theoretically to account for the effects of exogenous shocks on electoral expectations (Lupia and Strøm 1995; Diermeier and Stevenson 1999, (p. 792) 2000) It seems fair to expect that the exploration of informational effects will continue to be a major part of the literature on coalition politics.

4.3 Decision Rules, Institutions, and the Bargaining Environment

The third and final way in which subsequent scholarship has improved on Riker's conception of coalition politics is in its understanding of the bargaining environment, including the effects of political institutions. Fully capturing such influences required a shift in theoretical assumptions. Riker's work was based on cooperative game theory, with the specific bargaining process unmodeled. Such models generally assume that parties can make credible commitments and that the most “efficient” government will emerge. However, a substantial body of more recent scholarship has instead built on non‐cooperative game‐theoretic models, which focus on the incentives of individual parties and insist on a credible depiction of each stage of the bargaining process. By thus modeling the process of government formation, non‐cooperative models of government formation seek to understand bargaining dynamics in ways that cooperative models cannot capture. They also offer better ways to understand the importance of institutional rules that impinge on coalition bargaining.

The range of political institutions that may affect coalition bargaining is great, and political scientists have only begun to examine such effects systematically (for surveys, see Laver and Schofield 1990; Strøm, Budge, and Laver 1994; Strøm, Müller, and Bergman 2003). Institutions help define the formal requirements that government coalitions must meet, the process by which they form, the ways in which they can make policy, and the conditions under which they can be removed and replaced.

In the first place, constitutions differ in the demands that they place on incoming governments. Some national constitutions, such as those of Germany and Spain, feature a constructive vote of no confidence, which means that no change of government is possible unless the incoming government has a positive vote of support (an investiture) from a majority of the members of parliament. Other countries have formal investiture votes but no majority requirement (Italy), whereas yet others have no investiture requirement at all (Denmark). Bergman (1993) has explored the differences between positive (in which the incoming government must garner explicit majority support) and negative (in which there is no such requirement) parliamentarism and traced their consequences for coalition bargaining. When a formal investiture vote is required, coalitions are more likely to form. By forcing the parties in parliament to vote “Yeah” or “Nay” on each government at its very inception, investiture votes may render minority government less viable, and thereby make formal coalitions more likely to form. If there is a formal investiture vote, it is more difficult for a party tacitly to help keep a minority government in existence, yet to remain somewhat dissociated from it, so that the party can reject any (p. 793) responsibility for government policy and campaign against the incumbents in future elections.

Governments may also need to garner more than a simple majority in one chamber in order to “win” in coalition bargaining. In some countries the government is accountable to two chambers, so that what is a majority in one chamber may not suffice in the other. Druckman, Martin, and Thies (2005) report that the need to form a majority in a second chamber increases the likelihood of surplus coalitions.

The decision‐making environment within the executive branch may also affect coalition bargaining. Thus, Laver and Shepsle (1996) build on the literature emphasizing structure‐induced equilibria (Shepsle 1979; Shepsle and Weingast 1981), and argue that the set of cabinet portfolios and their respective jurisdictions decisively constrain the set of feasible policy options on which any coalition could agree, since it is difficult to prevent the holder of any given portfolio from implementing its own most preferred policy in that policy area. The data required to properly test the Laver and Shepsle model differ substantially from the type of data on government formation collected prior their work, so rigorous empirical testing of their approach has been limited (see however Warwick 1999; Laver and Shepsle 1999; Martin and Stevenson 2001). With more recent data collection efforts on portfolio allocation, however, further tests of portfolio allocation models can be anticipated. Research on Gamson's law concerning portfolio proportionality (e.g. Druckman and Warwick 2005; Warwick and Druckman 2001; Ansolabehere et al. 2005) and on the role of junior ministers (e.g. Thies 2001; Manow and Zorn 2004) has already built on this growing interest in portfolio allocation.

While most models assume that the set of relevant players includes only the parliamentary parties (or their leaders), institutional reality may be more complex. In semi‐presidential democracies, governments may not only be accountable to parliament or the legislature, but also to the president, which can significantly change the bargaining environment (Amorim Neto and Strøm forthcoming). Governments may also be interested in pursuing actions that require greater support than a simple majority in parliament allows. For example, a government may wish to enact a constitutional amendment that would require a legislative supermajority. To the extent that a simple majority is insufficient to satisfy the needs of its members, the likelihood of surplus majority coalitions increases.

Moreover, institutional rules governing the process of coalition bargaining may be of crucial importance. Of particular importance may be the rules designating the formateur, the person entrusted with the task of negotiating a coalition. Baron (1991) models this process (the recognition rule), considering both fixed and probabilistic sequences, and shows how varying the formateur sequence can have a large impact on the outcome. Subsequent work has shown that formateurs tend to receive a disproportionate share of office payoffs (Warwick and Druckman 2001; Ansolabehere et al. 2005), particularly when we consider not simply their shares of ministerial portfolios, but also the relative importance of the various ministries.

(p. 794) 5 Explaining Coalition Formation and Government Type

Bargaining models have thus tended to help improve our understanding of coalition formation by focusing on two different sets of factors: those relating to the bargaining environment and those relating to bargaining power. Both play an important role in explaining government formation in parliamentary democracies. A recent study of coalition formation in minority situations in Western Europe (Mitchell and Nyblade 2006), based on a particularly extensive set of data, finds both types of factors crucial in explaining whether ad hoc legislative coalitions or more formal executive coalitions form, and also in explaining the type of government that forms.

When government membership is more likely to cause serious costs to parties, formal executive coalitions are less likely to form. This may particularly be true when electoral volatility is high and when the previous government was terminated due to a critical event. Similarly, as opposition influence increases (when the relative benefits in policy influence of being in government decline), coalition formation becomes less likely. And in situations in which there is an inconclusive bargaining round—when parties specifically reject a potential coalition, indicating that their behavior is driven by more than simply the value placed on being in office—coalition government is less likely.

While the variables mentioned above capture the nature of the bargaining environment, the distribution of bargaining power amongst parties seems to have at least as large an impact on coalition formation. When bargaining power is disproportionately concentrated in the hands of a single party, even if that party does not have a parliamentary majority, single‐party government is more likely. A consistent finding throughout the history of coalition studies is that near‐majority parties are particularly likely to form minority governments (Strøm 1990a; Laver and Schofield 1990; Crombez 1996). Mitchell and Nyblade (2007) find, however, that the bargaining power of the largest party (as measured by the Banzhaf index) is an even better predictor of coalition formation than is its seat share.4 When the largest party has particularly large bargaining power (many potential partners with whom it can form winning coalitions, while it is more difficult to form winning coalitions without the party), it is much more likely to form a government on its own. Furthermore, when the largest party is also the median party in parliament, this effect is even more pronounced. Policy centrality in itself helps favored parties avoid broad coalitions.

Although most scholarship concerns itself with predicting minority and/or surplus governments as deviations from the norm of minimal winning coalitions, one could just as easily ask what makes MWCs more likely to form. Building on Riker's work, we (p. 795) expect MWCs to be most likely when the bargaining environment most closely resembles a simple cooperative bargaining model. Thus, when uncertainty is low, the value of government membership is high, and the decision rule is simple majority in a single chamber of parliament, MWCs should be most likely. Furthermore, following the logic of non‐cooperative bargaining models such as Crombez (1996) and Laver and Shepsle (1996), minimal winning coalitions should form when bargaining power is neither greatly concentrated in the hands of a single party (who then can form a minority government without incurring a great cost), nor so dispersed that a surplus government is formed in order to avoid the potential for blackmail. A president may complicate bargaining by dispersing bargaining power amongst more actors. So all else equal, MWCs may also be less likely in semi‐presidential or presidential systems.

Empirical analysis generally supports these suggestions (Mitchell and Nyblade 2007). In minority situations, minimal winning coalitions are more likely to occur when government is valuable: when opposition influence is low, electoral volatility low, and the previous government was not ended by a “critical event.” Minimal winning coalitions are also clearly related to the distribution of bargaining power in parliament. For example, when a “dimension by dimension median party” (cf. Laver and Shepsle 2000) exists that is quite small and has relatively weak bargaining power, it is especially likely to form a minimal winning coalition.

In contrast to minimal winning coalitions, minority governments have traditionally been seen as unviable and ineffective (Johnson 1975; Powell 1982). Yet, minority governments, as suggested above, need not be anomalies, and on many performance dimensions minority governments can be equal or superior to their majority counterparts (Strøm 1985). Not surprisingly, the factors explaining minority governments are quite similar to those that explain the lack of formal coalitions, since a large majority of minority governments are not coalitions. Empirical analyses suggest that, in addition to the two major factors identified in Strøm (1984) (electoral decisiveness and opposition influence), other measures that capture the relative value of office are important as well, such as the size and bargaining power of the largest party.

Surplus coalitions, on the other hand, generally have been understood as results of the inability of parties to credibly commit to each other. A minimal winning coalition can be brought down by any one of its members. So, if the parties do not trust each other, or cannot credibly commit to supporting each other over their term in office, they may find it useful to add a surplus member, so as to make it harder for one of the members to “blackmail” the government. This argument concerning surplus governments can be traced directly to Riker (1962), has been modeled more generally in theories of legislative logrolling (Carrubba and Volden 2000), and used to explain the creation of surplus governments in parliamentary democracies specifically (Carrubba and Volden 2004). The threat of blackmail is most acute when bargaining power is broadly dispersed amongst many parties; surplus governments are more likely to form in these cases. Mitchell and Nyblade (2007) find that surplus coalitions are also less likely when government membership is not particularly valuable, for example when electoral volatility is high, and when the previous government was terminated due to a critical event or policy conflict.

(p. 796)

In sum, both the bargaining environment and the distribution of bargaining power amongst political parties play a major role in determining the type of government formed. Minority governments are most likely to form when bargaining power is concentrated in the hands of a single party, when the costs of forming free‐floating coalitions are low, and when the value parties place on being in government is not too great. Minimal winning coalitions are most likely to form when the value parties place on being in government is high relative to being in the opposition, when uncertainty is low and parties are able to credibly commit to each other, when political decisions are made by simple majority rule, and when bargaining power is neither greatly concentrated nor greatly dispersed. Surplus coalitions are most likely when bargaining is greatly dispersed amongst the various parties in parliament, when political decisions require more than a simple majority in the lower chamber of parliament, and when government membership is neither extremely costly nor extremely valuable.

6 Government Membership

From the very beginning of the academic study of coalition government, scholars have been interested in predicting not only whether coalitions form, or the type of government formed, but more specifically which parties get into government. Riker suggested that the minimal winning coalition with the smallest parliamentary support—the minimum winning coalition—should form, while Leiserson (1966) instead proposed that the minimal winning coalition with the fewest members should prevail. Empirically, neither of these specific propositions has proven particularly robust in empirical testing.

Empirical scholarship on coalition formation has had greater success predicting specific government membership by focusing less on the office‐seeking models of coalition formation, and more on incorporating policy preferences. A first generation of analysis of “who gets in” in the 1970s generally came to contradictory results. Franklin and Mackie (1984) were the first to conduct multivariate tests in order to assess the relative importance of size versus policy preferences, and claimed to have reconciled the early research findings. They found that the wide discrepancy in previous studies was explained by methodological decisions such that the findings of Browne (1973) and De Swaan (1973) can be reconciled with those of Taylor and Laver (1973) “by simple adjustments of universe and weighting strategy” (Franklin and Mackie 1984, 681) and recognizing the existence of strong “country‐effects.” These authors go as far as to claim that in the work to date the “choice of countries is far more important than any other assumption in conditioning research findings” (Franklin and Mackie 1984, 671).5

(p. 797)

As statistical sophistication amongst political scientists has progressed, however, Franklin and Mackie's regression methodology has been criticized. Martin and Stevenson (2001) test a large sample of prior coalition propositions using more appropriate tools than heretofore. As they note: “The central shortcoming of [of prior approaches such as Franklin and Mackie's] is that in a regression framework & each potential coalition in a formation opportunity enters the estimation as a separate case. Thus, including countries such as Italy or Denmark, with a large number of parties at any given time, means that thousands of cases enter the estimation and completely swamp out relationships in other countries” (2001, 38). The answer, they suggest, is a maximum likelihood framework that models “government formation as an unordered discrete choice problem where each formation opportunity (not each potential coalition) represents one case and where the set of discrete alternatives is the set of all potential combinations of parties that might form a government” (ibid.). Martin and Stevenson use McFadden's conditional logit model, which is a special case of the multinomial logistic regression. Thus, potential coalitions are the discrete values that the dependent variable can take, and each potential coalition is associated with a set of size, ideology, and institutional variables that serve as the independent variables.

Martin and Stevenson find support for the effects of classic bargaining power variables (size and preference variables) as well as for bargaining environment variables such as investiture vote requirements, electoral pacts, and incumbency status. Overall, the predictive power of their models is fairly impressive (by the standards of prior work), with their best models accurately predicting the specific coalition formed (generally out of dozens or hundreds of potential coalitions) around 40 percent of the time, much greater than in previous empirical work on the subject (such as Laver and Budge 1992).

Recent work on “who gets in” builds on the Martin and Stevenson approach. Warwick (2005), with the help of an extensive expert survey, shows how information about the policy preferences of parties, beyond simple measures of their ideal points, improves our understanding of coalition politics. Warwick estimates the “policy horizons” of parties on multiple dimensions. These horizons are the points beyond which the parties are generally unwilling to compromise. Bäck and Dumont (2004) also employ the conditional logit framework as jumping‐off point, using the predictions made from these models to identify cases for more intensive study. From these case studies, they seek both to identify the causal mechanisms and in turn to generate ideas for variables that could improve the predictive power of empirical models.

7 Conclusion

The study of coalition governments has been one of the most active subfields in comparative politics, and one in which progressive improvements to both our theoretical and empirical knowledge have been most obvious. The study of government formation (p. 798) in parliamentary democracies has been intimately linked with bargaining theory, from the original works of Riker (1962) and Leiserson (1966), to theories incorporating policy preferences such as Axelrod (1970) and de Swaan (1973), through the development of more complex models that consider both (Austen‐Smith and Banks 1990) and often incorporate more of the bargaining environment, such as the influence of elections (as in Austen‐Smith and Banks 1988), or other institutional and behavioral constraints on potential coalition outcomes (see Strøm, Budge and Laver 1994). Despite the advances that have been made, however, there remain significant avenues for further research.

First, there is a need for theoretic work that more carefully integrates bargaining environment (institutions) and bargaining power (size, policy) variables. Austen‐Smith and Banks (1988) were pioneers in this regard, but much remains to be done. One promising line of research is that of Diermeier and his associates. Diermeier and Merlo (2000) develop a model of coalition formation in the shadow of future random shocks, following which the parties may respond by reallocating distributive benefits. Diermeier, Eraslan, and Merlo (2002, 2003) model how parties might evaluate tradeoffs between the size and durability of different types of coalitions during the coalition formation process, and how certain institutional rules and features (such as bicameralism, investiture votes, and constructive no confidence rules) may influence these tradeoffs and thus the likelihood of various types of coalitions.

Second, as in essentially every social scientific endeavor, critical measurement challenges remain. In the face of increasing evidence that policy preferences matter to coalition bargaining, coalition students were left with crude or awkward measures of such policy preferences, based either on subjective rankings or potentially on information inferred from the very behavior they sought to explain. In recent research, two primary strategies for overcoming these problems have been to generate policy estimates from expert surveys (as in Laver and Hunt 1992 and Warwick 2005), or from policy documents such as election platforms (manifestos). The latter approach can be traced back to the influence of Robertson (1976), but has been extended and regularized by the Manifesto Research Group (see Budge et al. 2001). There has been a vigorous debate about the challenges of estimating party policy positions (see Gabel and Huber 2000) and issue dimensionality (Warwick 2002; Nyblade 2004; Stoll 2005) from such data.

Finally, there are challenges in empirical tests. Studies of coalition bargaining have focused overwhelmingly on national governments in the stable parliamentary democracies of Western Europe. These data have been used, over and over again, to test and corroborate the major hypothesis of the field. There has, however, been very little testing that has gone much beyond the sample from which these propositions were derived. In future scholarship, this limitation clearly must be overcome. It is therefore most welcome to see several excellent studies of local and regional coalitions in parliamentary countries (Bäck 2003; Downs 1998), and we anticipate that the emergence of many new parliamentary democracies, especially in Central and Eastern Europe, will provide additional opportunities for rigorous tests of accepted wisdoms.

The challenges of empirical testing extend beyond issues of samples and case selection. There remain serious statistical challenges as well. For example, the conditional logit framework suggested by Martin and Stevenson (2001) rests on the statistical assumption (p. 799) of the independence of irrelevant alternatives (IIA), which in many cases may be problematic.6 Additionally, as coalition formation is but one stage in the life cycle of parliamentary government (Strøm, Müller, and Bergman 2007), and parties have both memory and foresight, it might be necessary in the statistical specifications to consider the other stages of government and selection effects, as in the structural estimation approach used by Diermeier, Eraslan, and Merlo (2003).

Although these theoretic and empirical challenges remain, we remain optimistic. Given the development of coalition research over the last forty years, and the continuing activity and innovation in this field, there is no reason to believe that our understanding of coalition politics should not continue to progress rapidly in the coming decades.

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                                                                                                                                                                          Notes:

                                                                                                                                                                          (1) Although one growth area in the study of coalitions is in considering the importance of intra‐party dynamics (Strøm 1994; Druckman 1996).

                                                                                                                                                                          (2) These data comes from Müller and Strøm (2000); Strøm, Müller, and Bergman (2007); and the analyses reported in this and subsequent sections draw on Mitchell and Nyblade (2007).

                                                                                                                                                                          (3) De Swaan stated his central behavioral assumption as follows: “An actor strives to bring about a winning coalition in which he is included and which he expects to adopt a policy that is as close as possible, on a scale of policies, to his own most preferred policy” (1973, 88).

                                                                                                                                                                          (4) The Banzhaf Power Index measures the ability of actors with differentially weighted vote shares to influence the outcome of a vote (Banzhaf 1965).The index calculates for each voter the proportion of potential vote combinations the actor is able to “swing” (change from winning to losing), relative to the ability of other actors to swing a vote. For example, in a 100‐seat legislature in which there are four parties, with 45, 26, 25, and 4 seats, if the decision rule is simple majority, the four‐seat party has no bargaining power because they are unable to change the outcome of any vote, as they cannot help form any minimal winning coalition.

                                                                                                                                                                          (5) In a study of cabinet duration, Grofman similarly claims that “the principal variation in cabinet durability appears to be generated by between‐country effects which are a function of party‐system variables such as the effective number of parties” (1989, 297–8, emphasis in the original).

                                                                                                                                                                          (6) A multinomial probit does not rest on the IIA assumption, and proper specification of a conditional version of this estimation technique may resolve this issue.