Cabinet payoffs in coalition governments

Abstract

Understanding how coalition parties in multiparty governments divide office and policy payoffs is one of the greatest challenges in political science. Gamson’s Law predicts that ministries are allocated proportionally with the coalition members’ legislative seat holding. However, doubts remain about how differences in the valuation of portfolios affect their distribution. The challenge is not only to determine whether government parties receive their fair share of cabinet payoffs once the importance of individual ministerial posts is taken into consideration, but also to develop a measure of portfolio importance that takes time and context into account. This article proposes a new method of measuring portfolio salience using official records of cabinet appointments in the Fifth French Republic that list ministerial posts hierarchically. The result is a more nuanced measure of portfolio importance, which is context sensitive and varies with time. The article argues that the new measure is able to reduce artificial deviations from the one-to-one linkage of seat shares and portfolio shares and that it can travel beyond the French case.

Keywords

cabinet rankings coalitions Gamson’s Law portfolio allocation portfolio importance

Introduction

The proportional distribution of ministerial portfolios in coalition governments is well known as one of the strongest empirical regularities in political science. Starting from Gamson’s (1961: 376) intuition that ‘any participant will expect others to demand from a coalition a share of the payoff proportional to the amount of resources which they contribute to a coalition’, political scientists have repeatedly confirmed the ‘iron law’ of proportionality between legislative seat shares and portfolio shares (De Winter and Dumont, 2006). Alternative operationalizations of party resources and coalition payoffs have also been introduced: bargaining power indices and minimum-integer voting weights were proposed as more appropriate proxies for the parties’ weight in national legislatures than their mere size (Shapley and Shubik, 1954; Banzhaf, 1965; Ansolabehere et al., 2005); while Druckman and Warwick (2005) and Druckman and Roberts (2008) derived measures of portfolio salience from expert surveys, so that a full test of the proportionality relationship that takes into account both quantitative and qualitative dimensions of ministerial payoffs can be carried out. However, none of these operationalizations alter the proportionality relationship significantly (Warwick and Druckman, 2006). The hypothesis that payoffs are more likely to mirror bargaining power than seat contributions is not supported by the new results either, as neither salience nor bargaining power seems to advantage ‘formateur’ parties (Warwick and Druckman, 2006: 652–658).

Comparatively fewer attempts have been made to challenge or refine the techniques used to capture variation in the importance of different cabinet seats. For example, the literature suggests that individual cabinet posts are not only valued differently by parties but their salience also varies from one election to another (Bäck et al., 2011; Raabe and Linhart, 2015). However, expert judgements of portfolio salience used for the weighting of ministries are unavoidably static, as they rely on a single estimate for each post and must assume that portfolio salience does not change over time (Warwick and Druckman, 2006: 641). Endogeneity problems may also emerge if expert judgements are influenced by the individuals or parties holding particular offices. Moreover, the further back into the past a study goes, the more difficult it is to estimate the importance of posts that existed only temporarily.

An alternative to expert surveys should be able to derive estimates of portfolio importance from context-sensitive sources that capture differences in the valuation of ministries from one cabinet to another. This is the aim of the current article, which studies portfolio allocation in the Fifth French Republic. Here, the appointment of new governments is accompanied by presidential decrees, which list cabinet members and departmental jurisdictions in a hierarchical order. As a result, official cabinet rankings are used to compute salience scores for individual portfolios in each government as well as average values of portfolio importance over the entire period under study. In this way, changes in issue and policy salience over time as well as short-lived posts can be taken into account.

Testing the proportionality relationship using the more nuanced measure of portfolio importance on an original data set of portfolio allocations in 37 French governments between 1959 and 2014 reduces the small-party bias almost completely, achieving an almost perfect one-to-one linkage of seat contributions and salience-weighted portfolio shares. This is a rather surprising finding in the French context, where the president’s strong influence over government formation might have been expected to skew the attribution of ministerial spoils in favour of her party. Quite the opposite, the results suggest that Gamson’s Law accuracy improves when context-sensitive sources are used to capture variation in portfolio importance compared to expert judgements. These findings indicate that nuanced measures of portfolio importance are able to reduce artificial deviations from the one-to-one linkage of seat shares and portfolio shares, providing an ideal setting to look for explanatory factors that account for substantial deviations from proportionality. The high correlation between average salience scores and expert estimates (Druckman and Warwick, 2005; Laver and Hunt, 1992) provides strong evidence that the context-sensitive, time-varying measure of portfolio importance is able to travel beyond the Fifth Republic case.

Measures of coalition payoffs and portfolio salience

The law-like nature of the proportionality relationship has been questioned by many authors. Browne and Franklin (1973) were the first to demonstrate not only the strong positive association between seat shares and portfolio shares in West European coalition cabinets but also a tendency for smaller parties to receive more than their proportional share of ministries. The small-party advantage was confirmed by Warwick and Druckman’s (2006) analysis on an extended data set of 14 European countries (1945–1999). Moreover, Bäck et al. (2009) revealed systematic deviations from proportionality in every country under analysis. Cross-country deviations from perfect proportionality of payoffs lead Indridason (2015) to argue that Gamson’s Law does not hold in its strict interpretation, which should see the linkage of seat shares and portfolios shares coming indiscernibly close to unity. This is only half of the story, though, as the varying degrees of importance between cabinet posts must be taken into account as well.

Finding ways to capture differences in the importance of ministerial departments has always been a challenge. Various functional criteria, such as parliamentary attention, media publicity and stepping stones for promotion and authority in cabinet have been used to identify high-status ministries (Rose, 1987: 84–92). Other authors derived hierarchies of cabinet posts from the ministers’ personal characteristics, such as age and parliamentary or cabinet experience (Dumont et al., 2009). In the absence of formal hierarchies of ministries, studies of cabinet payoff distributions posited a higher valuation of the prime ministership and a few other important portfolios such as interior, justice, agriculture, finance, foreign affairs and defence (Browne and Feste, 1975; Mesquita, 1979). One of their main limitations was the oversight of medium and low political status posts, which made it difficult to determine the exact size of the ministerial prize allocated to each coalition party. This weakness was addressed by Druckman and Warwick (2005), who carried out the most comprehensive expert measurement of portfolio salience in 14 West European countries over the post-war period. Subsequently, Druckman and Roberts (2008) provided expert ratings of portfolio salience in 14 Eastern European countries for the 1990–2002 period.

Despite the increasingly important role that expert surveys have come to play in political research, a number of questions about their accuracy have been raised. The general characterization of expert judgements as ‘fundamentally descriptive and static rather than analytical or dynamic’ (Budge, 2000: 104) is particularly problematic when it comes to measuring portfolio salience over a long period of time. As a matter of fact, measures based on a single estimate for each post must assume that portfolio salience is constant over time (Warwick and Druckman, 2006: 641). This may be a bold assumption for certain types of ministries. For example, the importance of the defence ministry is unlikely to have been constant during the Cold War and the post-1990 period. Moreover, similarly to party policy positions estimated by specialists, conducting a cross-national expert survey over a number of years means that some judgements are elicited during elections campaigns, while others are provided during inter-elections times (Budge, 2000: 110). Under these circumstances, it is difficult to know if specialist evaluations reflect issue salience in pre-electoral policy agreements or the importance of ministries based on the allocation of ministries to parties and individual politicians and how comparable these judgements are. This particular weakness has further consequences when the importance of temporary posts is inferred from the data by splitting or summing the ratings of components posts, as the new scores may cover different time periods than the specialists’ initial evaluation.

An alternative to estimating portfolio salience from expert surveys is to identify data sources that provide context-sensitive measures of portfolio importance that vary from one government to another. Cabinet membership lists that accompany the appointment of new governments can be used to extract this kind of information in many countries. Government composition is rarely listed in alphabetical order in official documentation, implying an informal hierarchy of some sort among cabinet posts. The formal order of ministers has legal and political consequences. For example, executive decrees accompanying the appointment of new governments in Portugal provide detailed information about the cabinet structure, the formal order of ministers and the competencies of each government department. Similarly, the appointment of French and Romanian governments is sanctioned by presidential decrees listing cabinet members and their departmental jurisdictions hierarchically. Cabinet reshuffles are also accompanied by executive decrees that signal changes in the initial order of ministries. In Turkey, cues about the hierarchy of cabinet members have been provided by the order of signatures on Council of Ministers’ decisions (Mutlu-Eren, 2015: 175, fn. 19). Another example where the hierarchy of ministers and ministries is obvious to the public is Greece, where ‘relatively high ranking often implies proximity to the prime minister, from which flows influence and autonomy’, while ‘one of the first things that some prime ministers do is to change the hierarchy of ministries in accordance with their outlook and priorities’ (Koutsoukis, 1994: 277–278).

The examples above suggest that researchers can use factual data to map the pecking order of cabinet posts. Access to official documents and other primary sources documenting the appointment of new governments can correct important shortcomings associated with expert judgements. First, the availability of data sources corresponding to individual governments can be used to establish fully comprehensive lists of ministries, including posts that existed only for short periods of time. Second, changes in the hierarchy of posts from one government to another can be used to compute importance scores that vary over time. A more finely grained measure of portfolio importance can be constructed in this way and used to highlight the political circumstances under which coalition parties receive more or less than their fair share of the ministerial prize.

Government formation and portfolio allocation in the Fifth French Republic

This article measures portfolio importance using formal cabinet rankings in the Fifth French Republic and tests the extent to which the distribution of salience-weighted ministries to coalition parties follows the proportionality norm. The Fifth Republic is one of the few countries where Gamson’s Law holds in its strict interpretation, according to which the slope coefficient and the intercept equal 1 and 0, respectively, with a high degree of statistical certainty.¹ This relationship is illustrated in Figure 1, which shows that the linkage of seat shares and portfolio shares comes closer to the one-to-one hypothesized relationship in France than in any other country in Western Europe. These are good circumstances under which one can test whether the allocation of portfolios continues to follow closely Gamson’s prediction when more nuanced differences in the importance of cabinet posts are taken into account.

Figure 1.

Portfolio share and seat contribution in 14 European countries (1945–1999). Source: Produced by the author on data from Warwick and Druckman (2006), inspired by Indridason (2015). The solid black line illustrates a perfect one-to-one relationship between seat contributions and portfolio shares. The solid red line corresponds to the ordinary least square (OLS) regression applied to France (1958–1997). Each of the dotted lines corresponds to an OLS regression applied to one of the remaining 13 European countries (1945–1999).

Another aspect that makes France a good case for this analysis is that cabinet formation in the Fifth Republic centres on the distribution of office spoils. The 1958 Constitution grants the head of state the power to select the PM and to appoint all other cabinet members on her proposal (article 8). Coalition building is short and, as noted by Thiébault (2000: 504), the only topic of discussion between the president, the PM and party leaders is portfolio allocation. Given the lack of a formal investiture requirement in parliament, the government officially exists from the presidential appointment act, which lists the names and jurisdictions of cabinet members in a hierarchical order. Nevertheless, due to the short formation period and the president’s influence on appointments, France is usually seen as a problem case of parliamentary coalition bargaining. The president’s authority over parliamentary parties has led scholars to doubt that legislative politics have an independent impact on the behaviour of the French executive (Laver and Schofield, 1990: 224–225). As a result, France has been excluded from many cross-country tests of coalition theories, including Browne and Franklin’s (1973) classic study of portfolio allocation.

There are several reasons why the president’s bargaining status might not be as problematic when it comes to the distribution of cabinet payoffs among coalition partners. To start with, more recent studies have emphasized the parliamentary logic of French institutional arrangements. For example, Huber (1996: 23–30) rebuffed both institutional and political arguments about the president’s primacy in French politics. He also dismissed the argument that France has produced stable and coherent majorities responsible to the president on empirical grounds: while a single party has rarely controlled a majority of seats in the National Assembly, the normal state of affairs in France has been that of incohesive majorities and ‘acrimonious coalition government’ (Huber, 1996: 29). Additionally, the president’s latitude in cabinet appointments and dismissals is constrained by legislative election results, especially during periods of divided government or cohabitation (Bucur, 2015; Thiébault, 2000: 503).

Second, although the presidents’ influence over government composition can hardly be questioned, especially during periods of unified government, their influence is mostly limited to their own party. Similarly to other parliamentary systems, where the government’s existence is subject to assembly confidence, coalition structures keep an important check on the powers of presidents and PMs. In other words, the fact that presidents control their party’s cabinet appointments does not prevent inter-party coalition negotiations over the number and policy areas allocated to each cabinet party. What explains the rapidity of the cabinet formation process is the existence of pre-electoral coalitions and the left–right bipolarization of the Fifth Republic’s party system (Thiébault, 2000: 506). Due to traditional alliances, coalition composition is not a question of post-election negotiation, unlike the division of portfolios. Policy negotiations also occur before legislative elections and have often taken the form of coalition agreements between traditional partners, such as the Socialists, left Radicals, and Communists on the left, and the Gaullists, centrists, and moderates on the right (Petry, 1987; Thiébault, 2000: 508–512). Post-election negotiations focus on the distribution of cabinet seats and take place between the parties in the winning coalition. Consequently, while the president’s preferences for the identity of the foreign and defence ministers and other non-partisan appointments limit the ministerial choices available to her party, they may not necessarily affect the cabinet seats quota allocated to coalition partners. Nevertheless, it could be the case that the president’s bargaining advantage in cabinet formation results in more important portfolios being allocated to the presidential party or assigned to non-partisan ministers. This is precisely one of the aspects that can be captured by a finely grained measure of portfolio importance.

A third factor enabling a systematic empirical analysis of cabinet payoffs despite the significant variation in the number and jurisdictions of ministerial departments over time are the presidential decrees that list cabinet members and their ministerial jurisdictions in a hierarchical order. The complexity of French cabinets is generated by the existence of different classes of ministers (Duhamel, 2011: 622). Apart from the prime minister and ordinary ‘Ministres’, cabinets may include ‘Ministres d’État’, the highest rank reserved for senior politicians, and ‘Ministres délégués’, who are usually responsible for specific domains within larger portfolios. The extended government structure may also include ‘Secrétaires d’Etat’ who do not normally sit at the cabinet table. Between 1959 and 2014, French cabinets averaged 23.4 members above the rank of state secretaries (2 state ministers, 15.6 ministers and 4.7 delegated ministers), of which 2.8 ministers were non-partisans. Figure 2 shows significant fluctuations in cabinet size. Given the frequent changes in the number and classes of ministers appointed to government, the value of individual posts is unlikely to be constant from one cabinet to another. Most departments are also affected by changes in the combination of policy domains and oscillations in the number of delegated ministers associated with them (Duhamel, 2011: 622–623).

Figure 2.

Cabinet size and classes of ministers appointed during the Fifth Republic (1959–2014).

The protocol order has political and legal consequences. Ministers are usually listed in accordance with their rank, which is also the order in which they can be asked to take over the cabinet when the PM is absent, and sit at the cabinet table according to an algorithm that follows the ordre protocolaire (Bonte, 2011: 26). When the cabinet is reshuffled, the new ranking provides straightforward information about whether ministers moved from one portfolio to another have been promoted or demoted in the cabinet pecking order. As a result, a party’s share of the ministerial prize can be re-estimated after each major cabinet reshuffle.

Cabinet rankings and portfolio importance

The following empirical analysis inquires whether a more nuanced way of weighting portfolios according to their position in formal cabinet rankings results in stronger seat–payoff proportionality. The following steps were taken to estimate a party’s share of ministerial payoffs in any given cabinet. A list of core posts that appeared in the composition of French cabinets between 1959 and 2014 was compiled using the presidential decrees published in the Journal officiel de la République française.² Following the procedure used by Warwick and Druckman (2006: 642), the importance of a portfolio that resulted from the combination of two or more posts was calculated as the sum of the importance scores obtained for separate posts. Ordinal rankings were then transformed into interval scores to assess relative differences between ministries. The following monotonically decreasing functions were evaluated for this purpose, where N denotes cabinet size and importance _i indicates the importance of the ith portfolio.

Reciprocal	$i m p o r t a n c e_{i} = \frac{\frac{1}{i}}{\sum_{k = 1}^{N} \frac{1}{k}} .$
Squared reciprocal	$i m p o r t a n c e_{i} = \frac{\frac{1}{i^{2}}}{\sum_{k = 1}^{N} \frac{1}{k^{2}}} .$
Linear	$i m p o r t a n c e_{i} = \frac{N + 1 - i}{\sum_{k = 1}^{N} (N + 1 - k)} .$
Exponential	$i m p o r t a n c e_{i} = \frac{e^{- λ i}}{\sum_{k = 1}^{N} e^{- λ k}} .$

The reciprocal function defines the importance of a portfolio as the inverse of its position in the ordre protocolaire. The linear function assigns linearly decreasing importance to all portfolios on the list, while the exponential one models portfolio importance as an exponentially decaying quantity. The decay rate λ is computed from the rank for which the importance ‘decays’ to half its initial value, that is:

λ = \frac{\ln (0.5)}{r a n k_{h a l f}} .

The exponential functions evaluated here halve the importance of portfolios after 12.5%, 25%, 50% and 75% positions in any given government (hereafter referred to as Exp_12, Exp_25, Exp_50 and Exp_75). All salience values are normalized to ensure that they add up to 1 in each government. Figure 3 shows how the importance of portfolios varies in a hypothetical 20-seat cabinet depending on which function is used.

Figure 3.

Conversion of cabinet rankings into interval scores using different functions.

Each function tells a different story about how negotiations over portfolio allocation may influence the variation in the importance of different ministerial positions. The reciprocal and squared reciprocal functions increase the difference between top and bottom posts at a much faster rate than the linear and exponential functions. As a result, while the importance of posts drops sharply in the first quarter of the cabinet hierarchy, differences between lower-end portfolios grow smaller as the size of the cabinet increases. For example, in a 20-seat cabinet the difference between the top and the bottom portfolio increases to 400 times when the squared reciprocal function is used, suggesting that a sharp decrease in importance down the pecking order is not a realistic assumption for a measure of portfolio salience. By comparison, the top portfolio is only 20 times more valued than the bottom one when either the reciprocal or the linear function is used to convert ordinal rankings into interval scores of importance. However, the top portfolio is 11 times more valued than the midlist portfolio for the reciprocal function and only 2 times more important for the linear function.

The exponential function allows one to decide how fast the difference between the importance of portfolios decreases. For example, halving importance one-eighth through the pecking order produces similar results as the squared reciprocal function. By contrast, when the importance of portfolios is halved midway and three-quarters through the pecking order, the ratio of the highest importance score and the lowest declines to 3.7 and 2.4 respectively. In both cases, the PM post is worth about two times the midlist position. This is a more likely spread of portfolio values, which eliminates unrealistically high disparities in portfolio values. Moreover, the scores obtained using the Exp_50 function come close to expert judgements, which value the top post five times and half more than the bottom portfolio in France (Druckman and Warwick, 2005: 27).

The presence of independent ministers introduces an additional problem. Previous studies of portfolio importance have excluded posts held by non-partisan ministers from the analysis to keep focus on partisan dynamics (Druckman and Warwick, 2005; Warwick and Druckman, 2006; Druckman and Roberts, 2008). This is not an option when portfolio payoffs are calculated on the basis of cabinet rankings, which include both partisan and non-partisan ministers. Excluding independent members from these lists would artificially boost the importance of coalition payoffs obtained by parties, as the importance measures used here are non-linear. An alternative way of keeping non-partisan positions in the analysis without compromising the one-to-one proportionality of seat shares and cabinet shares is to assume that the number of independents is known before the remaining seats are distributed among coalition partners. In this case, the expected value of cabinet seats allocated to a party is computed as a percentage of the total number of cabinet seats (i.e. including independents). The benefit of keeping independent ministers in the data set is that importance values can be computed for the full list of ministerial posts. In any coalition cabinet that includes non-partisan ministers, the sum of all parties’ qualitative shares of cabinet portfolios is one minus the portfolio share allocated to independent ministers.

Two types of importance scores were calculated on the basis of formal rankings: single estimates for each portfolio in any government and mean estimates for the entire period of time a given portfolio appeared in government. To obtain separate scores for different posts when they are combined into a single portfolio, the total score was split equally. The importance of each post was then averaged over the entire period of time to obtain a salience measure similar to those presented by Druckman and Warwick (2005). The mean value of a portfolio that combined two or more posts is obtained by summing up the mean values of the respective posts. Average values for all cabinet posts (including standard errors, standard deviations, and the number of their occurrence in the data set) are presented in the Appendix 1 of this article. This list is fully comprehensive and includes every post that appeared in government between 1959 and 2014. However, further analyses must be undertaken to demonstrate the validity of the new scores.

First, the new measure’s comprehensiveness can be judged against the five properties of a valid measure of portfolio salience identified by Druckman and Warwick (2005: 34): cross-national scope, country-specific measurement, coverage of the full set of post-war portfolios, measurement by multiple experts and measurement at interval level. Bar cross-national scope, all other criteria are met: the importance scores cover all cabinet portfolios that appeared in government since the beginning of the Fifth Republic and provide interval-level values derived from a large number of cabinet-specific sources. Additionally, this measure is sensitive to variation in the valuation of posts from one government to another.

Second, the viability of salience scores is established in relation to Druckman and Warwick (DW) (2005) ratings and Laver and Hunt (LH) (1992) rankings. Correlations between the mean importance scores produced by the seven functions and the measures provided by DW and LH³ along with two-tailed p values and the number of portfolios compared in each case are presented in Table 1. Correlations with DW ratings are very high, ranging between 0.65 and 0.83. Rank-order correlations with LH rankings are not as high, averaging about 55%, but higher still than the correlation between LH and DW rankings for French portfolios. As Druckman and Warwick (2005: 28) noted, most of this discrepancy is caused by the environment portfolio, which was ranked as the second most salient by Laver and Hunt (1992). The high association between the importance scores derived from factual data and the salience estimates provided by expert surveys provides strong reasons for confidence in the comprehensiveness and reliability of both measures.

Table 1.

Reliability of portfolio importance scores.

Function	Average importance (SD)	Minimum importance	Maximum importance	Correlation with DW			Correlation with LH
Function	Average importance (SD)	Minimum importance	Maximum importance	Coefficient	Significance	n	Coefficient	Significance	n
Reciprocal	0.021 (0.031)	0.005	0.260	0.79	p ≤ 0.00	26	0.55	p ≤ 0.04	14
Squared reciprocal	0.007 (0.030)	0.000	0.260	0.73	p ≤ 0.00	26	0.67	p ≤ 0.01	14
Linear	0.023 (0.017)	0.017	0.083	0.75	p ≤ 0.00	26	0.56	p ≤ 0.04	14
Exponential halved at 12.5%	0.021 (0.030)	0.001	0.214	0.83	p ≤ 0.00	26	0.54	p ≤ 0.04	14
Exponential halved at 25%	0.022 (0.020)	0.004	0.121	0.81	p ≤ 0.00	26	0.55	p ≤ 0.04	14
Exponential halved at 50%	0.024 (0.014)	0.009	0.078	0.73	p ≤ 0.00	26	0.52	p ≤ 0.06	14
Exponential halved at 75%	0.024 (0.012)	0.010	0.066	0.65	p ≤ 0.00	26	0.55	p ≤ 0.04	14

Note: The mean importance score for each post was calculated first, then the average, standard deviation, maximum and minimum importance scores were determined across all posts. The minimum, average and maximum importance values for a sample of individual posts obtained with the Exp_50 function are presented in Figure 4. Standard errors, standard deviations and the number of times each post occurs in the data set are presented in Appendix 1.

Source: Compiled by the author following Druckman and Warwick (2005).

Figure 4.

Portfolio importance scores in the Fifth French Republic (1959–2014). Importance scores determined by Exp_50.

Third, the reliability of the new importance measure can be assessed by considering how much portfolios vary in salience and whether this variation follows the patterns previously suggested in the literature (Druckman and Warwick, 2005: 29). The data presented in the first three columns in Table 1 indicate a relatively large spread between the average values of minimum and maximum importance, regardless of the function used to compute these scores. For reasons of comparability with previous estimates of portfolio salience emphasized above, a more detailed analysis of variation across portfolios is provided just for the range of values produced by the Exp_50 function.⁴ The minimum, average and maximum importance scores of a set of portfolios that appeared in at least five governments are plotted in Figure 4. The mean scores confirm previous cross-country analyses, which singled out defence, finance, economics, foreign affairs, education, interior and agriculture as the next most important posts after the prime ministership (Browne and Feste, 1975; Browne and Frendreis, 1980; Laver and Schofield, 1990; Mesquita, 1979). More specifically, the mean values of portfolio importance plotted in Figure 4 indicate that the prime ministership is followed in the order of importance by the justice, defence, foreign affairs, finance and economy and interior ministries. Their average salience scores are clearly distinctive, while the importance of remaining portfolios decreases smoothly.

Does the new measure of portfolio salience pass the proportionality test?

The empirical test needed to answer this question is carried out on a data set that covers the distribution of 866 portfolios among 94 parties that participated in 37 governments between 1959 and 2014. Data on seat shares are collected from the Parliamentary Debates part of the Official Journal of the French Republic (1958–2014), which publishes the number and names of deputies who join parliamentary party groups (PPGs). The size of PPGs is a good indicator for the number of seats controlled by large parties. However, not all parties are able to form autonomous PPGs, as the statutes of the French National Assembly require a minimum participation threshold.⁵ Parties falling behind this threshold have usually had to choose between formally adhering to one of the existing PPGs as associated members or joining forces with other small parties to form political groups of an exclusively parliamentary nature (Avril and Gicquel, 2010: 101). Left-wing Radicals have often joined the parliamentary group of the Socialist Party (PS), their closest political ally. In 1997, however, the Radical Party of the Left (PRG) together with the Green Party (PV) and the Citizen and Republican Movement (MDC) formed a separate group called ‘Radical-Citizen-Green’ (RCV), despite lacking a common political ideology. Similarly, the Greens and Communists formed a common parliamentary group in 2002 under the name of ‘Democratic and Republican Left’ (GDR). Therefore, taking parliamentary groups as an expression of unitary parties may lead to arbitrary decisions about the numerical and political composition of coalition governments.⁶ To avoid this kind of problems, the number of seats corresponding to each party is recorded in the following way: the size of government parties represented by autonomous PPGs in the national assembly is recorded as the total number of deputies affiliated with the respective party groups, including both party members and associated members; when two or more parties from the same parliamentary group are in government, party sizes reflect the exact number of deputies corresponding to each party (i.e. PS and MRG/PRG during 1981–1986, 1988–1993, 2012–2014; PV, MRG/PRG and MDC during 1997–2002).

Previous studies have called attention to portfolio ‘lumpiness’, or the need to allocate whole posts to single parties, as a potential cause of systematic deviations from perfect proportionality. Estimating the parity prediction as a linear relationship between party resources and ministerial payoffs generates some random errors because seat shares and portfolio shares are expressed in different units. To address this problem systematically, one can turn to proportional representation rules, which provide a handy solution for the distribution of portfolios in multiparty executives.⁷ Divisor rules, such as d’Hondt or Sainte-Laguë, have been used to determine not only the number of posts each party receives but also a sequencing procedure that determines the order in which parties choose their preferred ministries in Northern Ireland and in some Danish municipalities (O’Leary et al., 2005). Country-by-country tests indicate that using these methods to smooth out the allocation process has a negligible effect on the proportionality relationship.⁸ Moreover, the Sainte-Laguë allocation method is seen as ‘the unique unbiased proportional divisor method’ (Balinski and Young, 1982: 125). Consequently, one can operationalize the independent variable of party resources as the share of cabinet portfolios that a government party would be predicted to receive if the Sainte Laguë algorithm were used to translate legislative seat shares into cabinet shares.

Two dependent variables are used in the statistical analysis. The first one is the unweighted share of cabinet portfolios and the second one is the salience-weighted share of cabinet posts obtained by a coalition party. The results corresponding to ordinary least square (OLS) analyses of the relationship between party size and coalition payoffs are given in Table 2. The first row tests the relationship between seat shares and unweighted portfolio shares and finds an even stronger association between the two variables compared to Warwick and Druckman’s (2006) results. The slope coefficient is 0.96 and the intercept is 0.01, suggesting that the proportionality norm has strengthened in the last two decades. Moreover, F statistics and associated p values for the null hypothesis that the seat share coefficient and the intercept equal 1 and 0, respectively, confirm the high probability that the allocation of portfolios is strictly proportional.

Table 2.

Legislative seat shares and ministerial shares.

Dependent variable	Constant		Coefficient (adjusted seat share)		R ²	No. of parties	F value	p value
Portfolio share (unweighted)	0.012*	(0.006)	0.966***	(0.019)	0.962	94	2.78	0.0753
Salience-weighted portfolio share (importance scores vary across governments)
Reciprocal	−0.028***	(0.008)	1.077***	(0.020)	0.941	94	8.85	0.0007
Reciprocal2	−0.076***	(0.013)	1.221***	(0.035)	0.838	94	24.04	0.0000
Linear	−0.004	(0.008)	1.003***	(0.022)	0.957	94	0.50	0.6095
Exp_12	−0.028	(0.009)	1.069***	(0.026)	0.932	94	4.7	0.0153
Exp_25	−0.010	(0.007)	1.020***	(0.022)	0.955	94	0.94	0.4001
Exp_50	0.001	(0.007)	0.993***	(0.019)	0.963	94	0.37	0.6901
Exp_75	0.005	(0.006)	0.983***	(0.019)	0.965	94	0.62	0.5423
Salience-weighted portfolio share (importance scores averaged across governments)
Reciprocal	−0.024***	(0.009)	1.067***	(0.026)	0.943	94	3.910	0.0291
Reciprocal2	−0.063***	(0.013)	1.186***	(0.037)	0.852	94	15.880	0.0000
Linear	−0.001	(0.009)	1.002***	(0.027)	0.956	94	0.02	0.9814
Exp_12	−0.018*	(0.010)	1.049***	(0.030)	0.943	94	1.79	0.1817
Exp_25	−0.006	(0.009)	1.016***	(0.027)	0.955	94	0.28	0.7601
Exp_50	0.000	(0.008)	1.000***	(0.025)	0.959	94	0.01	0.9942
Exp_75	0.002	(0.008)	0.995***	(0.024)	0.960	94	0.13	0.8828

Note: Results from ordinary least square (OLS) regressions where the independent variable is a party’s seat share (adjusted by Sainte-Laguë formula) and the dependent variable is its unweighted (Model 1) or salience-weighted (Models 2–15) share of cabinet portfolios. F statistics and p values reported for the null hypothesis that the seat share coefficient equals 1 and the constant equals 0. Standard errors in parentheses (clustered by government).

*p < 0.10; **p < 0.05; ***p < 0.01.

The next models estimate the relationship between seat shares and weighted portfolio shares. First, we consider how the importance of portfolios varies from one government to another. In this case, the dependent variable is the salience score determined by each of the seven functions used to convert ordinal rankings into interval scores (i.e. reciprocal, reciprocal squared, linear, Exp_12, Exp_25, Exp_50, Exp_75). A party’s salience-weighted portfolio share is computed as the normalized sum of the average salience scores of all its portfolios and varies from one cabinet to another depending on the number of posts received and on their position in the official rankings. The results show that not every importance measure provides as good a model fit as the original specification. Specifically, only Exp_50 and Exp_75 increase the level of variance explained by the model and only linear and exponential functions (except for Exp_12) pass the F-statistic test. Finally, the results indicate that deviations from perfect proportionality are almost eliminated in the case of Exp_50, where both the slope and the intercept come very close to 1 and 0, respectively.

Similar results are obtained when portfolio importance values are averaged across all governments in the data set. The last seven rows in Table 2 indicate that the relationship between seat shares and weighted portfolio shares approximates perfect proportionality when the importance of portfolios is halved midway through the formal ranking (Exp_50), as the slope and intercept virtually reach the hypothesized values of 1 and 0, respectively. This result is also supported by the F-statistic test. These are encouraging findings, indicating that measures of qualitative portfolio payoffs derived from factual data have a good chance of reducing the small-party bias almost completely, providing an ideal setting to look for explanatory factors that account for systematic deviations from proportionality.

The way in which portfolio importance reduces the small-party bias is explained by the case of parties with a small seat share that receive one extra post. For example, consider the case of the Green Party in the Socialist-led cabinet formed by Jean-Marc Ayrault in May 2012. Although the 2% share of parliamentary seats this party brought to the government coalition entitled it to one portfolio according to the proportionality norm, the Greens received two seats at the cabinet table. Taking a close look at the positions of the two portfolios in the cabinet hierarchy reveals a high qualitative difference between them, as they were placed 7th and 31st in the 35-seat cabinet. Thus, the contribution of the second portfolio to the coalition payoffs obtained by the party was double the amount of its fair share of the ministerial prize in quantitative terms but rather negligible when considered in terms of its importance. A similar situation occurred in June 1988, when the left-wing Radicals were allocated the 4th and 27th positions in Michel Rocard’s 27-seat cabinet. These examples show that while the small-party bias cannot be eliminated completely, using an appropriate function to estimate the actual importance of ministerial prizes can significantly reduce the artefact generated by the distribution of extra portfolios with a negligible importance. This is also a way to minimize the impact of ‘artificial ministries’ on the fixed total value of the ministerial prize when new offices are established simply to increase the number of available jobs and ease the formation of a coalition (Budge and Keman, 1990; Indridason and Bowler, 2014; Verzichelli, 2008).

Conclusion

The qualitative dimension of portfolio allocation or the ‘who gets what’ question lies at the heart of coalition bargaining (Browne and Franklin, 1973: 478). A growing body of literature highlights the importance of capturing variation in how different cabinet posts are valued in order to understand coalition politics outcomes. For example, accounting for portfolio salience when testing the proportionality relationship could vindicate bargaining models by showing that formateur parties receive a disproportionate share of valuable cabinet posts (Warwick and Druckman, 2006). A salience measure is also needed to determine if parties are driven by the objective importance of portfolios or by their ideological preferences when allocating cabinet positions (Bäck et al., 2011; Ecker et al., 2015). Devising such a measure is, however, a challenging task.

Expert survey-based measures of portfolio salience have enabled some of the first systematic attempts to explore the quantitative and qualitative aspects of coalition payoffs (Druckman and Roberts, 2008; Warwick and Druckman, 2006). Nevertheless, the validity of expert judgements has been criticized for being static, descriptive and susceptible to endogeneity problems (Budge, 2000). This article proposes an alternative to expert surveys, which derives estimates of portfolio importance from context-sensitive sources. The resulting measure captures changes in the value of ministries from one cabinet to another over the entire period under study.

In France, as in many other countries, information about the relative differences between cabinet posts can be found in the ordres protocolaires that accompany the appointment of each new government and list cabinet members and their policy jurisdictions in a hierarchical order. These documents were used to compile a fully comprehensive list of French ministries in the Fifth Republic (up to 2014). Further on, salience scores for single posts in each government as well as average portfolio scores across the time period under study were computed using different functions to convert ordinal rankings into interval scores of portfolio importance. The new measure was tested on an original data set of portfolio allocations in 37 governments in the Fifth French Republic (1959–2014). The results show an almost perfect one-to-one linkage of seat contributions and salience-weighted portfolio payoffs, improving the proportionality relationship between seat shares and portfolio shares. The new model reduces the small-party bias almost completely and provides an ideal setting to look for factors that account for substantial deviations from the proportionality norm under different political circumstances.

The strict proportionality of portfolio allocation in the Fifth French Republic may appear as a surprising result, given the presence of a head of state with a constitutionally strong role in government formation. More work is needed to explore competing hypotheses about how presidents influence the distribution of ministerial spoils in parliamentary systems. On the one hand, the increase in bargaining power associated with the presidency could lead to expectations that, to the extent that deviations from proportionality exist, they advantage the president’s party. Conversely, if one adheres to Charles de Gaulle’s conception of a presidency ‘above parties’, then the proportionality of party resources and coalition payoffs could be the deliberate result of presidential action. One way forward in researching how or whether presidents influence portfolio allocation would be to use process-tracing methods along the lines suggested by Bäck and Dumont (2007) and compare cases that are well predicted by the proportionality relationship with deviant cases from the one-to-one linkage of seat shares and portfolio shares. The method of process induction could then be used to discover new explanatory variables that are able to shed more light on the role played by heads of state in the formation of coalitions and the distribution of cabinet positions.

The existence of ministerial rankings in other countries means that the importance measure can travel beyond the case of France. The method of estimating time-varying measures of portfolio importance put forward in this article applies to coalition governments in parliamentary and semi-presidential systems but may also extend to presidential systems, given the rise of ‘coalitional presidentialism’ (Power, 2010). Taking into account both quantitative and qualitative aspects of portfolio allocation might be of particular interest for empirical tests of institution-based portfolio allocation models across parliamentary and presidential systems (Indridason, 2015). Cross-temporal variation in the importance of individual ministerial posts could also be used to test whether institutionally strong presidents and/or PMs are more likely to take advantage of their positions to change the hierarchy of ministries according to their policy priorities.

The link between cabinet rankings and policy payoffs points towards the limitations and directions for future research that could be explored using time-varying estimates of portfolio importance. To a certain extent, the pecking order of portfolios tells a partial story of the coalition bargaining process. The rankings are endogenous to the formation process and inter- or intra-party negotiations between political heavyweights take place behind closed doors. Therefore, sometimes it is difficult to tell if changes in the protocol order of ministries reflect new policy priorities or the strong bargaining position of important politicians. The answer is probably somewhere in the middle. We know that while ideological preferences matter when coalition partners bargain over ministerial posts (Bäck et al., 2011), parties are also driven by the ‘market value’ of cabinet positions (Ecker et al., 2015: 813). Moreover, Bäck et al. (2011) suggest that policy-seeking parties may accept less than their fair share of the prize if they capture those ministries with a higher policy value for them; while other parties’ policy payoffs may be reflected in coalition agreements despite not receiving their preferred portfolios. One potential avenue for further research would be to study if the trade-off between policy-valued posts and ministry-specific salience is reflected in the pecking order of portfolios. Alternatively, one could check the match between the formal ranking of ministries and the emphasis laid on corresponding policy issues in coalition agreements. Altogether, providing variation in both policy payoffs and general portfolio importance from one cabinet to another opens more opportunities to uncover national and cross-national determinants of portfolio allocation.

Footnotes

Acknowledgements

The author wishes to thank Paul Warwick for making available the data set on portfolio allocation in post-war Western European governments. Special thanks to Bjørn Erik Rasch, Shane Martin, Thomas Meyer and participants to the ‘Making and Breaking Coalition Governments’ panel at the 2015 Annual General Conference of the European Political Studies Association in Vienna for helpful comments on an earlier version of this article.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Norwegian Research Council [grant number 222442 (FriSam Project)].

Supplemental material

Supplementary material for this article is available online.

Notes

Appendix 1

Table 1A.

Portfolio importance scores in the Fifth French Republic (1959–2014).

Post	Mean	SD	SE	N
PM	0.078	0.022	0.004	37
No portfolio	0.070	0.007	0.003	6
Algerian affairs	0.063	0.000	0.000	1
Justice	0.062	0.020	0.003	38
Defence/army	0.053	0.015	0.003	36
Foreign	0.052	0.018	0.003	40
Interior	0.047	0.021	0.003	39
Education	0.038	0.015	0.002	39
Relations with parliament	0.038	0.016	0.003	24
Overseas	0.037	0.017	0.003	25
Culture	0.034	0.025	0.004	32
Social affairs	0.033	0.021	0.005	17
Environment	0.031	0.012	0.002	28
Cooperation	0.030	0.021	0.005	21
Planning	0.029	0.010	0.003	9
Immigration	0.029	0.012	0.007	3
Solidarity	0.028	0.015	0.004	14
Agriculture	0.028	0.014	0.002	37
Constructions	0.027	0.002	0.001	3
Reforms	0.026	0.024	0.005	20
Economy	0.026	0.009	0.001	40
Privatization	0.025	0.001	0.001	2
European affairs	0.025	0.009	0.002	22
Budget	0.025	0.010	0.002	23
Finance	0.024	0.008	0.001	39
Foreign trade	0.024	0.011	0.003	20
Spatial planning	0.023	0.012	0.002	34
Security	0.023	0.004	0.002	5
Veterans	0.023	0.006	0.001	20
Industry	0.023	0.008	0.001	39
Energy	0.022	0.013	0.006	5
Research and technology	0.022	0.009	0.001	36
Health	0.022	0.010	0.002	30
School education	0.022	0.007	0.004	4
Post and telecommunications	0.022	0.007	0.002	21
Transports	0.021	0.015	0.003	31
Labour	0.021	0.009	0.002	31
Women	0.021	0.013	0.004	10
Civil service	0.020	0.014	0.003	21
Integration	0.020	0.011	0.004	9
Public works	0.020	0.012	0.002	27
Decentralization	0.020	0.009	0.002	20
University	0.019	0.007	0.002	15
City	0.019	0.008	0.002	13
Atomic/space affairs	0.019	0.009	0.003	10
Information/communication	0.019	0.005	0.001	26
Family	0.018	0.011	0.004	9
Housing	0.017	0.006	0.001	29
Employment	0.017	0.009	0.002	20
Leisure	0.017	0.007	0.004	3
Development	0.016	0.012	0.004	10
Humanitarian action	0.016	0.001	0.001	2
Population	0.016	0.006	0.002	8
Sports	0.015	0.007	0.001	23
Fisheries	0.015	0.007	0.002	11
Social cohesion	0.015	0.003	0.001	4
Urbanism	0.015	0.006	0.003	5
Elderly	0.015	0.007	0.003	4
Training	0.014	0.006	0.002	11
Forestry	0.014	0.004	0.002	6
Francophony	0.014	0.006	0.002	9
Youth	0.014	0.004	0.001	22
Social economy	0.013	0.004	0.003	2
Repatriates	0.013	0.012	0.008	2
Tourism	0.013	0.004	0.001	19
Sea	0.013	0.007	0.002	10
Numeric economy	0.013	0.006	0.003	4
Spokesperson	0.012	0.003	0.001	13
Trade	0.012	0.004	0.001	23
Food	0.012	0.002	0.001	10
Handicrafts	0.012	0.004	0.001	22
Disabled	0.011	0.005	0.002	5
Youth employment	0.011	0.004	0.003	2
Diaspora	0.010	0.003	0.002	2
Consumer	0.010	0.004	0.002	3
Small and medium enterprises	0.009	0.002	0.001	6

Note: Scores determined using the Exp_50 function.

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