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Coalition Inclusion Probabilities:A Party-Strategic Measure for Predicting

Policy and Politics ∗

Mark A. Kayser†Matthias Orlowski‡Jochen Rehmert§

This version: 23 April 2020

Abstract

Policy in coalition governments depends on negotiations between parties, a factthat extant measures of electoral competitiveness intended to predict policy fail torecognize. We conceptualize, estimate, validate and make available a novel measureof parties’ bargaining leverage intended to help predict policy and politics. We arguethat those parties with the greatest leverage in policy negotiations are those with thehighest probability of participating in an alternative government, were one to form.Combining a large set of political polls and an empirical coalition formation modeldeveloped with out-of-sample testing, we estimate coalition inclusion probabilitiesfor parties in a sample of 21 parliamentary democracies at a monthly frequencyover four decades. Applications to no-confidence motions and to the stringency ofenvironmental policy demonstrate our measure’s utility and superiority over the onlyother measure of electoral competition available between elections, vote intentionpolls. (142 words)

World count: 9,410

Keywords: coalition bargaining, electoral competitiveness, policy-making

∗Previously presented at the ECPR 2016 Joint Sessions, Pisa, MPSA 2017, EPSA 2018, APSA 2019and the Europe Center, Stanford University. We kindly thank Jon Fiva, Evenlyn Hübscher, Rene Lind-städt, Lanny Martin, Thomas Sattler and Georg Vanberg for helpful comments. We further thank LannyMartin, Anthony McGann, Will Jennings, Christopher Wlezien and Christopher Wratil for sharing datawith us. Mark Kayser and Jochen Rehmert gratefully acknowledge support from the German FederalMinistry for Education and Research (BMBF), grant number 01UF1508.†Hertie School of Governance, Berlin, [email protected]‡areto consulting, gmbh, [email protected]§Humboldt University of Berlin, [email protected]

Coalition Inclusion Probabilities

1 Introduction

How do parties translate public preferences into policy in multiparty systems? The link

between public preferences and government actions lies at the heart of democratic gover-

nance, leading generations of scholars to investigate questions of policy representation and

responsiveness. A large majority of this research, however, focuses on countries charac-

terized by single-party governments, such as the United States, the United Kingdom and

Canada.1,2 In coalition governments, public opinion also influences parties’ policy pref-

erences but the implementation of any coalition member’s preferences into actual policy

requires an extra step: coalition bargaining.

Before now, no strategically-oriented, dynamic and empirically validated means of

predicting which party’s preferences will emerge as policy has existed. Some scholars, of

course, have nonetheless analyzed the influence of public preferences and policy outputs

in multiparty systems (e.g., Klemmensen and Hobolt, 2005; Wlezien and Soroka, 2012)

but they have done so by neglecting the policy bargaining stage. Scholars wishing to

acknowledge that parties’ policy preferences do not translate directly into policy outputs in

multiparty governments had only two choices: (1) they could turn to static seat allocation

rules (e.g., Gamson, 1961) and/or bargaining power indices (Shapley and Shubik, 1954;

Banzhaf, 1964) or (2) posit that parties’ standing in the polls or shifts in public opinion on

specific issues over time alter the balance of power in coalition governments (e.g., Lupia

and Strøm, 1995).

We draw on key insights from both of these approaches to develop a novel measure of

bargaining leverage in coalition governments. Like Shapley and Shubik (1954), we argue

that bargaining leverage arises from credible threats to quit the government and, like Lupia

and Strøm (1995), we argue that the credibility of such threats varies dynamically over

the life of a government as external circumstances and polls change. We differ, however,1see Wlezien and Soroka (2016) for a review.2Other factors include data availability, language barriers, and the focus of many European researchers

on the particulars of European Union policy-making.

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by arguing (and demonstrating) that shifts in party polling and public opinion are not

sufficient to change bargaining outcomes and, hence, policy. Shifts in polling only change

bargaining leverage and policy outcomes when they also change a coalition member’s

ability to exit for an alternative government. Thus, what matters in dynamic negotiations

over policy in coalitions is how changes in external polls effect parties’ probabilities of

inclusion in alternative governments: coalition inclusion probabilities.

We also differ from these previous literatures in our empirical focus. We build an

empirical coalition formation model that we optimize for prediction with out-of-sample

testing and then apply to a large sample of polls. We can thus predict the probability of

every possible coalition that could form and then sum by party to calculate the probability

of each party joining government. Although numerous alternatives are possible, this

paper calculates two types of coalition inclusion probabilities (CIP) for most parties in

21 parliamentary democracies at a monthly frequency for all periods in which data exist

between 1970 and the 2018. The first, gross CIP, is the probability for each party in the

parliament of joining a government, were a new one to form. This captures the general

importance of each party in terms of coalition formation. The second, net CIP, is the

probability of each party joining a government that excludes a specific party – the prime

minister’s party – and is intended to capture leverage over the prime minister’s party.3

The result, we argue, is a set of measures that, in combination with other variables

such as issue salience, should enable scholars to better predict political behavior and pol-

icy outcomes in multiparty governments. We demonstrate our measures’ utility with two

distinctly different applications – no-confidence motions and the stringency of environ-

mental policies – and contrast the performance of CIP with weak results from two naïve

alternatives that neglect coalition bargaining, political polls and public opinion.3For prime minister parties, net CIP is calculated vis-a-vis the largest junior coalition party.

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2 How to predict policy

2.1 Public opinion

Scholars have made large strides explaining and predicting policy in settings with single-

party governments. Research on the United States, United Kingdom and Canada has

shown that public preferences on issues generally cluster across issues, suggesting a single

underlying preference for government action (Stimson, MacKuen and Erikson, 1995) but

also that some salient issues can deviate and influence policy (Druckman and Jacobs,

2006), that policy mood responds to the economy (Durr, 1993), that policy change often

precedes changes in public opinion (Page and Shapiro, 1983), that governments shift

policy dynamically in response to public opionion between elections (Stimson, MacKuen

and Erikson, 1995), and that policy and public opinion interact ‘thermostatically’ with

each influencing the other (Wlezien, 1995; Soroka and Wlezien, 2010).

Research that addresses multi-party systems, however, has yielded notably fewer and

less precise findings predicting policy outcomes. We do know how broad policy outcomes

differ in systems with single-party and multi-party governance – policy responsiveness

is slower (Wlezien and Soroka, 2012) in many of the countries in which policy changes

come in infrequent but large clusters (Baumgartner et al., 2009) – but more fine-grained

questions of which party successfully implements its preferred policy and in what circum-

stances elude us.

So, why does policy research do so much better in single-party government settings?

The reason, we argue, is that predicting policy from coalition governments requires un-

derstanding the bargaining leverage of the parties, a step that is not necessary with

single-party governments. Interestingly, one important and highly visible finding that

does address policy outcomes in multiparty systems posits coalition negotiations and

compromise as the reason why policy outcomes in coalition governments hew closer to

the public opinion preferences of the median voter in proportional than in majoritarian

electoral systems (Huber and Powell, 1994; Powell, 2009). What they do not address,

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however, is how coalition members reach a compromise. It is precisely this process and

how it influences policy in favor of which actors that we seek to address here theoretically

but, most importantly, through the creation of a new tool.

2.2 Elections and polls

Electoral competitiveness, like public opinion, also serves frequently as a predictor of

policy. In contrast to public opinion that usually concerns a particular issue, however,

electoral competitiveness is most often associated with how well, closely or quickly gov-

ernments respond to a valence issue or shift policy toward the preferences of the greatest

number of voters. Politicians elected in competitive settings, for example, purportedly

respond more to their median constituents (Ansolabehere, Snyder and Stewart, 2001),

moderate their partisan preferences in fiscal policy (Solé-Ollé, 2006) and spend more on

public goods (Hecock, 2006).

Measuring electoral competitiveness, however, is not so straight-forward. The strong

overrepresentation of single-country studies in research related to electoral competitive-

ness, most notably the United States and other countries with frequent single-party gov-

ernment, is likely a result of the ease of measuring it with two-party vote, poll or seat

margins in such systems.4 The dependence of vote margins on the number of parties in

the system makes it an awkward measure for cross-national samples that include multi-

party systems. Given that a minority of developed democracies host two-party systems,

cross-national research entails developing a measure of electoral competitiveness that also

captures patterns of party competition in multi-party systems.

Recently, a few cross-national measures have emerged, each presenting a distinct way

of conceptualizing and measuring multi-party competition electoral vulnerability (Abou-

Chadi and Immergut, 2014), seat plurality loss probability (Kayser and Lindstädt, 2015),

bargaining power categories (Abou-Chadi and Orlowski, 2016) and electoral availability4Kayser and Lindstädt (2015), for example, find that 21 of 29 articles related to electoral competi-

tiveness in three top political science journals in a five year window focus on a single-country.

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(Wagner, 2017). Predicting party preferences, however, is not the same thing as predicting

policy. Regardless of how well electoral competitiveness predicts parties’ policy positions,

even in multiparty systems (see, e.g., Adams, 2012) it does not and can not address the

fact that policy outcomes in most coalition governments are the outcomes of coalition

bargaining rather than the preferences of any single party. In other words, an intervening

and crucial step – coalition bargaining – exists between electoral competitiveness (usually

based on vote, seat or polling outcomes) and policy in multiparty systems with coalition

governments.

Nor can one simply assume that increases in vote, seat or poll shares will map mono-

tonically onto the probability of a party advancing its preferred policy. For example, one

strong – but not exclusive – factor for influencing policy is inclusion in government but

simply increasing vote and seat share will not necessarily increase a party’s chance of

gaining office or making policy. A party that shifts from the third to the second largest

seat share in a parliament, for example, might actually reduce its probability of govern-

ment inclusion because the largest party might, following Gamson’s law, prefer the third

largest party as a coalition partner in order to dole out fewer portfolios. What matters

for predicting policy and parties’ behavior, we argue, is often not polls, vote shares, seat

shares, measures of electoral competitiveness or even public opinion but the specific set

of coalition formation options and bargaining leverage that parties hold.

2.3 Bargaining power

Many factors influence parties’ policy preferences but what matters for policy-making

when multiple parties with differing policy preferences are in government is bargaining

leverage. And key to bargaining leverage, we argue, is a credible exit option. When

a party can credibly threaten to abandon the government for an alternative governing

coalition, especially one that excludes the leading party, it has considerable influence.

This assertion is not novel. The authors of several voting power indices, following a

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similar logic to ours, have generated algorithms to calculate the power (weight) of each

vote (party) as a function of its probability of it causing a coalition to form or fail by

switching (Penrose, 1946; Shapley and Shubik, 1954; Banzhaf, 1964). Exit threat is the

key idea of voting power indices (e.g., Banzhaf, 1964) and scholars have previously asserted

that coalition members’ leverage depends on outside options (Becher and Christiansen,

2015) and forward-looking strategic calculations (Lupia and Strøm, 1995).

We build on the logic of Lupia and Strøm (1995, e.g., p. 649) who posit that bargain-

ing in coalitions over the life of a government is influenced by changes in parties’ standings

in the polls: “The anticipation of good electoral fortunes gives a party a bargaining chip

that it can exploit by either negotiating the balance of power within an existing coalition,

forging a more attractive coalition with new partners, forcing dissolution and new elec-

tions, or protecting the existing cabinet.” What is new, however, is our contention that

parties’ leverage does not rely on anticipated electoral performance but, more specifically,

on how such an electoral performance would translate in to coalition options.

So why not simply employ an existing measure of bargaining power such as that

from Shapley and Shubik (1954) or Banzhaf (1964)? Such theoretical models usually

calculate coalition probabilities from party seat shares and ideological distance which,

though certainly important, contrast markedly with empirical models (e.g., Martin and

Stevenson, 2010) that find that factors such as anti-establishment parties and similarity

with the previous coalition matter roughly as much. Empirical models, for their part, do

a fair job of predicting coalition composition by including more variables but they ignore

individual party-level coalition inclusion probabilities and are not designed for out-of-

sample prediction. Moreover, both types of models, by relying on measures derived from

or temporally near elections, implicitly assume that politics stop between elections or, at

least, that bargaining leverage does not change.

To remedy these problems, we develop a party-level measure of “coalition inclusion

probabilities” (CIP) that is both dynamic – measured monthly between elections – and

optimized for out-of-sample prediction. By combining coalition formation models with

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(an immense amount of) polling data to predict exit leverage (net CIP) at a monthly

frequency, we are offering the first empirical measure that can evaluate theoretical claims

about dynamic coalition bargaining. Coalition inclusion probabilities (CIP) matter for

parties not only because they are a direct measure of the chance of inclusion in government

but also because, for coalition members, they measure the credibility of an exit threat.

Theoretically, it is possible to create many different types of CIPs depending on the

party with which a given party is bargaining. For the sake of practicality, however, we

create only two types. Gross CIP is the simple expected probability of a party being

included in a government; net CIP captures negotiating leverage in the form of a party’s

expected probability of inclusion in an alternative coalition that excludes the current

prime minister’s party or, in the case of the prime minister’s party, a government that

excludes the largest junior party.

In order to estimate the probability of any party’s inclusion in government, we must

first estimate the probability of various governing coalitions forming. While previous

empirical research has estimated models that fit the data well, no published work has (a)

extracted the party-level coalition inclusion probabilities, (b) tested predicted coalition

formation out of sample, and (c) done so dynamically between elections.5 Our measure

offers all of these properties at a monthly frequency in 21 developed democracies for all

years with polling data since 1970 and additionally distinguishes between gross and net

CIP.

3 Design

3.1 Empirical strategy

We follow a three-step procedure to assess the implications that polls have for any party

to enter government. First, we estimate a conditional logit model of coalition forma-5One prescient paper, however, has estimated the probability of parties being included in each of two

possible governments in Iceland in one formation opportunity by summing up the probabilities of allgovernments in which they might be included (e.g., Glasgow and Golder, 2015).

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tion that builds on the findings of influential scholars of coalition formation (Martin and

Stevenson, 2001, 2010). We choose government and party samples identical to theirs and

replicate their specifications as a benchmark. We then modify them to maximize model

performance both in and out of sample. Our sample in this step, like theirs, excludes

formation opportunities in which a single party holds a majority.

Second, we expand our sample to include more recent as well as single-party majority

formation opportunities. We employ a parsimonious variant of the model selected in the

previous step in order to minimize the loss of observations from missing data. We again

test the performance of our model out of sample but at the party level as well as the

coalition level.

Finally, in a third step, we calculate predicted probabilities at monthly frequency for

government formation, treating polls as if they were in fact a correct description of the

partisan composition of the respective legislature – a reasonable assumption in our sample

of proportional electoral systems. Each possible governing coalition receives a predicted

probability, which then allows us to sum up, for each party, the probabilities of each

possible government in which they are included.

With applications to no confidence votes and environmental policy, we demonstrate

the comparative usefulness of CIPs relative to polls – the main alternative measure of

party fortunes that varies between elections, but one which does not capture the coalition

calculus of parties.

3.2 Data and variables

Our analysis relies on two datasets: one containing information on the party composition

of governments and legislatures in 31 parliamentary democracies6 between 1947 and 20186Australia, Austria, Belgium, Canada, Denmark, Finland, Germany, Greece, Iceland, Ireland, Italy,

Japan, Luxembourg, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, and the UnitedKingdom, as well as Bulgaria, Croatia, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland,Romania, Slovakia and Slovenia.

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and one containing aggregates of different monthly polls since 1970 in 21 countries.7 We

draw on data on parliaments and governments provided by Döring and Manow (2016) and

on parties’ ideological position (Volkens et al., 2015)8 to assemble the first. Jennings and

Wlezien (2016) collected the original polling data for the second, which we then extended

where possible (see the list of alternative sources in Online Appendix A). Our end result

is gross and net CIP measures for the countries, parties and years listed in Table 1.

Table 1: Coverage of CIP Estimates

Country Period Parties

Austria 1995,1997,1999-2018 BZÖ, Dinkhauser, FPÖ, Greens, LIF, NEOS, ÖVP, PILZ, SPÖ, Stronach

Czech Republic 1993-2018ANO, CSSD, KDU-CSL, KSCM, LSU, ODA, ODS

Pi, SPD, SPR-RSC, STAN, SZ, TOP09, UPD, US, VV

Denmark 1970-2018 A, CD, DF, DKP, En-O, FK, FrP, KF, KrF, NLA, RF, RV, Sd, SF, V, VS

Estonia 2007-2018 EER, EK, ERa, ERe, EV, IRL, SDE|M

Finland 1994-2018 DL|VAS, KESK, KOK, RKP-SFP, Rt, SKL|KD, SP|P, SSDP, UV, VIHR

Germany 1970-2018 AfD, CDU|CSU, FDP, Greens, PDS|Linke, SPD

Greece 1994-1995, 2007, 2009-2018AE, Dimar, DISY, EK, KKE, LAOS, LE, LS-CA

ND, PASOK, POLAN, SYN, SYRIZA, TP

Hungary 2000-2018 Fidesz, DK, Eygyutt, FKgP, Jobbik, LMP, MDF, MIEP, MSZP, SzDSz

Iceland 1994-2018 A, Ab, BF, B-H, Dawn, F, Ff, Graen, HG, IDP, KL, M, Pi, Rebo, Sam, Sj, Th-Ff, V

Ireland 1974-2018 DLP, FF, FG, Green, IA, Lab, PD, SF, United Left

Italy 2000-2018AN, CD, FdI-CN, FdV, FI, IdV, IET, LeU, LN, M5S, MAIE, NCD

NcI, PD, PdCI, PdL, PoUD, PRC, RI, SC, SEL, SVP, UDC, USEI

Japan 1998-2018 CGP, DPJ, JCP, JReP, CDP, LDP, LP, NPD, NPN, PFG, PH, PLFP, PNP, SDP, YP

Netherlands 1970-201850+, AOV, ARP, Bp, CD, CDA, CHU, CP, CPN, CU, D66, DENK, DS70, FVD

GL, GPV, KVP, LN, LPF, NMP, PPR, PSP, PvdA, PvdD, PVV, RPF, SGP, SP, VVD

New Zealand 1996-2018 A, ACT, Greens, LP, Mana, MP, NP, NZFP, PP, UFNZ

Norway 1970-2018 DLF, DNA, Fr, H, KrF, MDG, RV, SF, Sp, SV, V

Poland 1993-2018D|W|U, AWS, BBWR, ChD, K, KLD, Korwin, KPN, LPR, N, NCDBdP, NSZZ

PC, PiS, PL, PO, PSL, Razem, RdR, ROP, RP, SDPL, SRP, UP, UPR, X, ZChN

Portugal 1985-2018 BE, CDS-PP, CDU, PRD, PS, PSD

Slovakia 2004-2018ANO, HZDS, KDH, KLsNS, KSS, MH, OLANO

S, SaS, SDKU, Smer, SMK-MKP, SNS, SR

Slovenia 1996-2018DeSUS, DL, L, LDS, LMS, LZJ-PS, NSI, SDS, SLS

SMC, SMS, SNS, ZaAB, Zares, ZdLe, ZL-SD, ZS

Spain 1980-1982, 1984-2018AP-P, BNG, CC, CDC, CDS, CiU, C-PC, EHB, ERC

P, PCE|IU, PNV, PSOE, UCD, UPyD

Sweden 1970-2018 C, FP, LD, MP, MSP, NyD, SAP, SD, V

7Austria, Czech Republic, Denmark, Estonia, Finland, Germany, Greece, Hungary, Iceland, Ireland,Italy, Japan, the Netherlands, New Zealand (post-1996), Norway, Poland, Portugal, Slovakia, Slovenia,Spain, and Sweden.

8More specifically, we compute parties’ logrile-scores as detailed in Lowe et al. (2011).

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Our dataset for the first step – our analysis of government formation – contains 121,276

potential cabinets that could have formed in 502 different formation opportunities, i.e.

either post-election or post-cabinet termination bargaining situations as defined by Martin

and Stevenson (2001).9

Each potential cabinet is described by a set of binary variables indicating whether it

is the status quo cabinet, a minority government, or a minimal winning coalition. Other

dummy variables encode whether the largest, the median and/or the previous prime min-

ister party are part of a potential cabinet, and whether or not it contains at least one

anti-system party (see Abedi, 2004).10 Following Martin and Stevenson (2001, 2010), we

also include a set of continuous predictors that characterize each potential cabinet. While

the number of parties in a potential coalition proxies the heterogeneity of its members’

preferences arithmetically, the ideological range in the coalition and in opposition do so

on substantive grounds. The same holds for the anti-establishment preferences in the

coalition, which is the maximum value of the sum over four items11 in the manifesto data

for the parties in the coalition.

Besides the status quo indicator, three additional variables capture the role of history

in predicting future governments. In their attempt to disentangle different sources of in-

cumbency advantage in government formation (preference familiarity, inertia, bargaining

costs, and incumbents’ procedural privileges), Martin and Stevenson (2010) introduced

two new variables that capture the similarity between a potential cabinet and the status

quo government on a continuous scale and the familiarity of any pair of parties in the9We excluded formation opportunities where caretaker governments took office as well as those where

we lack information on important covariates for parties that together held more than 5% of legislativeseats. In all other cases, we deleted parties with missing information from a formation opportunity beforecomputing the corresponding potential cabinets.

10Abedi classifies a party as anti-system if: (a) it challenges the status quo of major policy and politicalsystem issues, (b) it perceives itself as a challenger to established parties, and (c) it asserts that a cleardivide between the political establishment and the people exists (Abedi, 2004). Abedi’s data have beenupdated by Loomes (2012). We use both datasets as well as Hanley and Sikk (2016) for Central Europeancountries for our coding.

11These are a party’s view on the constitution (per204), on political corruption in the country (per304),and its evaluation of the national way of life (per602) and traditional morality (per604).

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potential cabinet. Similarity is the absolute difference in parties’ Gamson scores12 when

comparing a potential cabinet to the incumbent coalition. It thus captures not only the

overlap between the two cabinets in terms of partisan composition but also differences in

parties’ relative size (Martin and Stevenson, 2010). The more similar a potential coalition

is to the incumbent coalition, the lower the corresponding bargaining costs, and the more

likely it is to form.

Martin and Stevenson’s familiarity measure captures the notion that common govern-

ment experience facilitates coalition bargaining between any pair of parties. The more

parties in a potential coalition that have previously governed together, the easier it is for

them to form a coalition. Dissent, especially that leading to coalition dissolution, is also

not so quickly forgotten (Tavits, 2008). Arguing that more recent and longer experiences

should matter more than more distant ones, Martin and Stevenson (2010) suggest com-

bining the share of days that any pair of parties had governed together using a weighting

scheme according to which the contribution of common government experience on famil-

iarity decreases with time. Because party leaders change, on average, after eight years in

Western European parties, in computing their measure, Martin and Stevenson completely

discount common government experience that lies further in the past.

Unaltered party leadership, however, is not the only mechanism that preserves com-

mon government experience and facilitates coalition bargaining among former partners.

Personnel below the formal party leadership are involved in coalition negotiations as they

also are in the everyday business of joint government. The duration of an entire party

career therefore seems to be a more sensible benchmark for choosing a rate of decay for

common government experience. Consequently, we constructed a measure for each poten-

tial cabinets’ common history. Past governments contribute to the common government

experience of some subset of parties in a potential cabinet. By computing the share of

parties in a potential cabinet that were part of a particular previous government, we deter-12A party’s Gamson score is the share of legislative seats that it contributes to all seats held by the

parties in government.

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mine the size of this subset. Summing up these scores over all past governments weighted

by their duration in days, again, is a first indicator of a potential cabinet’s shared history.

We then set an exponential decay rate such that after 50 years, approximately the max-

imum length of a political career, less than one percent of the information a particular

historic government provides for the common history of potential cabinets remains.

Following Martin and Stevenson (2010), we also include a set of variables describing

the broader bargaining context. Two binary indicators describe the institutional con-

text capturing governments’ investiture requirements13 and the existence of post-election

continuation rules.14 Additional dummy variables indicate whether the formation op-

portunity took place after a general election and whether or not the incumbent cabinet

dissolved due to public intra-cabinet conflict.15 We rescaled all continuous variables to

range from zero to one.

In evaluating particular hypotheses about coalition formation, it is common and ap-

propriate to exclude formation opportunities in majority legislatures from the data. In

order to evaluate our predictors’ influence on coalition formation and benchmark our

model against previous models in the literature, we initially follow this standard and ex-

clude 130 formation opportunities in which a single party held an absolute majority of

legislative seats. Our interest here, however, is not only in evaluating the undistorted

effect of particular covariates on coalition formation but to derive parties’ expected prob-

ability of entering government correctly from polls. We therefore later reintroduce the

majority legislatures.

For our particular purpose – creating CIP measures that themselves can predict politi-

cal and policy outcomes – it is important to avoid fitting noise in the data. Consequently,

we evaluate models by randomly selecting and setting aside about 20 percent of our

(non-majority situation) data (18,100 potential cabinets in 62 formation opportunities)13Positive parliamentarism per Bergman (1995).14Incumbent parties are collectively given the first shot at building a new government after an election.15Data come from Woldendorp, Keman and Budge (2013) with updates by Seki and Williams (2014).

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for out-of-sample predictions. This leaves us with 79,084 observations in 262 formation

opportunities in a training set.

4 Model estimation

4.1 Step 1: Models of coalition formation

Our first step is to select a model that builds on the findings of the empirical coalition

formation literature and performs as well as possible in and out of sample. Following

Martin and Stevenson (2001), we model the probability of exactly one potential cabinet

forming out of all possible cabinets that could potentially form at a particular formation

opportunity. Hence, for a legislature containing p parties, we estimate the probability

that exactly one of 2p−2 potential coalitions forms.16 In this set-up, the interdependence

implied by choosing one government alternative over another is accounted for by treating

formation opportunities as the units of analysis and the potential governments as the

respective choice sets (Martin and Stevenson, 2001, 2010; Glasgow, Golder and Golder,

2012).

Table 2 presents the coefficient estimates for four conditional logit models of coalition

formation with formation opportunities as observations and potential coalitions as the

choice set. Model 1 is a naïve model with a minimal set of key predictors; Model 2

follows Model 7 reported in Martin and Stevenson (2001); and Model 3 mimics the main

model (i.e., Model 3) in Martin and Stevenson (2010). Model 4 adds our new indicator

of common government history, variables for anti-system as well as the second and third

largest parties and replaces the RILE (i.e., CMP) measure of ideological distance with one

based on party families. Although we run these models on data largely self-collected, we

rely for some covariates on replication data from Martin and Stevenson (2010). In order16Note that the total number of potential coalitions that could form in a legislature with p parties

is in fact 2p − 1. Following the standard approach in the literature, however, we exclude the coalitionof all parties as a possibility assuming that there will always be at least one party in opposition to thegovernment in democratic polities.

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to level the playing field and to compare the performance of models estimated on the

exact same sample, we restrict the estimation to data with full coverage on all covariates

(i.e., 20 OECD democracies, 1947-2010).

The naïve model based on predictors capturing the effects of the largest party, ideolog-

ical division and the status quo of potential coalitions confirms conventional expectations

about coalition formation: the largest party is more likely to enter a coalition, which in

turn is more likely to form if all parties in the coalition are ideologically close to each

other or if the potential coalition happens to be the outgoing one. We can, as Model 2

shows, largely reproduce the results of Martin and Stevenson (2001) using our data. This

does not, however, hold for the findings reported in Martin and Stevenson (2010) and

replicated in Model 3. Adding the factors that distinguish the different sources of incum-

bency advantage and that more thoroughly describe the bargaining context offers little

additional insight. Most coefficient estimates of the new terms in Model 3, in contrast to

those in Model 2, remain statistically insignificant.

The final model in Table 2 replaces Martin and Stevenson’s familiarity score with our

new measure of potential cabinets’ common government experience, the logRILE measure

of ideological distance with one based on party family, and the anti-establishment index

by a binary variable indicating whether an anti-system party as defined by Abedi (2004) is

included in a given potential coalition. Furthermore, we add two indicators for the second

and the third largest party in parliament, as we expect that the chances of the third largest

party, the “kingmaker”, trump that of the second largest party. By using the party families

and anti-system parties we can overcome some of the data shortages associated with the

CMP-based variables, which often do not exist for smaller and fringe parties, especially in

earlier elections. Moreover, the CMP-based anti-establishment preference variable does

not account for how a party’s anti-establishment standing is perceived by other parties.

This sort of pariah-status is better captured by Abedi’s classification.

For the new ideological distance variable, we follow König, Marbach and Osnabrügge

(2013) and order party families along a latent left-right dimension. In this ordering,

14


Table 2: Models of coalition formation

Naïve MS 2001 MS 2010 New(1) (2) (3) (4)

Minority Government −0.815∗∗ −0.833∗∗ −0.660(0.393) (0.414) (0.542)

Minimal Winning Coalition 0.309∗∗ 0.295∗ 0.486∗∗∗

(0.154) (0.167) (0.155)Number of Parties in Coalition −0.544∗∗∗ −0.566∗∗∗ −0.049

(0.106) (0.130) (0.115)Largest Party in Coalition (LP) 1.580∗∗∗ 1.593∗∗∗ 1.608∗∗∗ 1.078∗∗∗

(0.172) (0.225) (0.232) (0.298)Median Party in Coalition 0.452∗∗ 0.448∗∗ 0.537∗∗∗

(0.192) (0.197) (0.190)Ideological Range in Coalition (log RiLe) −7.485∗∗∗ −5.715∗∗∗ −5.755∗∗∗

(0.721) (1.091) (1.113)Ideological Divisions within Majority Opposition (log RiLe) −0.629 −0.368

(0.990) (1.009)Previous PM Party in Coalition (PM) −0.112 −0.864∗∗ −0.783∗∗

(0.228) (0.385) (0.377)Status Quo 3.088∗∗∗ 2.612∗∗∗ 1.831∗∗∗ 1.705∗∗∗

(0.166) (0.207) (0.458) (0.439)Minority Government with Investiture Requirement −0.015 0.011 −0.537∗

(0.313) (0.317) (0.300)Anti-Establishment Preference in Coalition −3.112∗∗ −3.245∗∗ −0.923

(1.266) (1.291) (1.208)Anti-Pact associated with Coalition −2.335∗∗∗ −2.358∗∗∗

(0.402) (0.402)Pre-Electoral Pact associated with Coalition 4.483∗∗∗ 4.664∗∗∗

(0.766) (0.790)Familiarity −0.009

(0.742)Similarity 1.343∗∗ 0.879

(0.530) (0.545)Intracabinet Conflict × SQ −0.355 −0.115

(0.502) (0.449)Intracabinet Conflict × PM 0.373 0.112

(0.435) (0.407)Postelection Bargaining (PE) × SQ 0.533 0.613

(0.432) (0.406)Average Seat Change (SC) 0.034 0.043

(0.047) (0.050)SC × PE 0.004 0.018

(0.058) (0.059)SC × SQ −0.012 0.028

(0.070) (0.071)SC × PE × SQ 0.023 −0.034

(0.082) (0.082)Anti-System Party in Coalition −2.083∗∗∗

(0.352)Second Largest Party 0.188

(0.221)Third Largest Party 0.801∗∗∗

(0.208)Cabinet History 2.590∗∗∗

(0.514)Ideological Range in Coalition (Party Families) −0.647∗∗∗

(0.091)Ideological Divisions in Majority Opposition (Party Families) 0.067

(0.103)Countries 20 20 20 20Formation Opportunities (in-sample) 262 262 262 262Observations 79,084 79,084 79,084 79,084R2 0.008 0.010 0.010 0.011Max. Possible R2 0.028 0.028 0.028 0.028Log Likelihood −798.910 −720.441 −714.103 −657.767LR Test 609.260∗∗∗ (df = 3) 766.198∗∗∗ (df = 13) 778.875∗∗∗ (df = 22) 891.547∗∗∗ (df = 23)

Note: Conditional logit with formation opportunities as observations and potential coalitions in choice set.∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.

15


Communist/Socialist parties are on the far left and receive a value of 1, Green/Ecologist

receive a 2, Social Democratic parties are on rank 3, Liberal in the middle category of

4, next to Christian Democrats on 5 and Conservatives on 6. Nationalist or right-wing

parties are on 7. To calculate the ideological range, we just take the absolute difference

between the two coalition parties that are farthest apart. Data on the party families stems

from ParlGov and CMP, for such parties belonging to the Agrarian party family or that

are coded as special issue parties, we looked into their international party group affiliation

and/or which parliamentary party group they have joined in the European parliament to

approximate their ideological position.17

The estimates suggest that history indeed matters for the formation of new cabinets.

Model 4 shows that the more frequently a large set of parties within a potential cabinet

has recently governed together, the more likely these parties are to eventually form a

government. Additionally, being the third largest party in parliament is significantly as-

sociated with government formation lending some credibility to the common “kingmaker”

analogies.

As argued above, the predictive quality of the model for coalition formation is of par-

ticular concern in the context of deriving a predicted probability for parties’ participation

in government from polling data. The Cox and Snell R2 values reported in the table pro-

vide some indication regarding the in-sample predictive performance of the four models.

The maximum possible value depends on the model’s functional form and is reported in

the table as well. Comparing the R2 values of the four models shows that the additional

regressors in Models 3 do not substantially improve the in-sample predictions. The pre-

dictive performance of all four models is only modest. Roughly speaking, the models

achieve only between 30 (Model 1) and 40% (Model 4) of the explanatory power that a

perfectly predictive conditional logit model would have for the data at hand.

17König, Marbach and Osnabrügge (2013) have also shown that parties’ left-right positions do notchange as dramatically over time as the highly volatile CMP RILE scores suggest.

16


Table 3: Coalition level confusion matrix excluding majority situations

Naive Model MS 2001 MS 2010 Newnot realized realized not realized realized not realized realized not realized realized

not_realized18,004 34 18,003 35 18,001 37 18,006 32(0.998) (0.548) (0.998) (0.565) (0.998) (0.597) (0.998) (0.516)

realized34 28 35 27 37 25 32 30

(0.002) (0.452) (0.002) (0.435) (0.002) (0.403) (0.002) (0.484)Precision 0.452 0.435 0.435 0.484Recall 0.452 0.435 0.435 0.484Note: All models estimated on a training dataset excluding single-party majority situationsand predictions tested out-of-sample. Column percentages in parentheses. Precision = T P

T P +F P ;Recall = T P

P .

What matters most for our purposes is to predict correctly the formation of govern-

ments beyond the data we used to estimate the coefficients. Table 3 displays the confusion

matrices for out-of-sample point predictions for the 62 randomly selected formation op-

portunities that we set aside as a testing set. Each confusion matrix is based on the

predictions derived from Models 1 through 4 in Table 2. For each formation opportunity,

we predict the potential government to form for which the predicted probability is the

highest. Hence, if there are not two potential governments for which we get the same

predicted probability at the highest value, we obtain exactly 62 positive predictions. The

rows of Table 3 depict our predictions, while the columns report potential governments

that actually formed or not. Hence, while the downwards diagonal of the matrices contain

the correct predictions, the upward diagonal reports the false negatives and false positives,

in that order.

The out-of-sample predictive performance mirrors the modest in-sample performance

of the models. We only predict between 40 and 45% of coalition governments correctly

in the first three models and the true positive rate improves only slightly (to 48%) when

adding the indicators for common history, anti-establishment and second and third largest

parties in Model 4. Prima facie, these findings suggest that, despite the development of a

sophisticated theoretical and empirical literature, our true understanding of government

formation in non-majority legislatures remains rather limited.

17


4.2 Step 2: A general model of government formation

Having developed a model that out-performs those of Martin and Stevenson using their

sample coverage and, like them, excluding majority government formation opportunities,

we now add majority governments, slim down the model and test it against the alternative

models in- and out-of-sample at the most relevant level for our purposes, the party level

rather than the coalition level.

While the exclusion of formation opportunities in which a single party held the major-

ity of legislative seats is appropriate for testing hypotheses about coalition formation and

benchmarking against previous models in the literature, it is less helpful for our purposes.

After all, we are interested in the implications that polls have for the formation of any

type of government, including single party majority cabinets. Hence, if polls indicate

that a single party is likely to obtain the majority of legislative seats, in order to get the

probabilities of ending up in government for all other parties right, we need to know the

odds that the majority party will eventually govern alone.

We therefore fit an additional model to a dataset including formation opportunities in

majority situations. As most of our indicators are expected to behave differently under

majority and non-majority situations, we introduce interaction effects to account for the

predictors’ possible diverging effects in these situations. Model 1 in Table 4 includes the

key variables from Model 4 in Table 2, interacted with non-majority situations.18 In order

to assess the predictive quality of this model, we again randomly sampled 80 percent of

the formation opportunities, now including majority situations, into a training data set

onto which we fit the model. As it contains only a subset of the set of previous predictors

we denote this model New_parsimonious or New_par.

At the coalition level, the new parsimonious model (Model 1, Table 4) outperforms

the others in- and out-of-sample (see Appendix Table B1) but those are also the wrong18For practical reasons, we dropped predictors that can safely be regarded as non-confounders on

theoretical grounds, offer little predictive value, and are laborious to collect such as anti-establishmentpreferences or institutional rules describing the bargaining context.

18


Table 4: A general model of government formation (New_Par)

Coeff. S.E.Largest Party in Coalition 0.744∗∗ (0.299)Single Party Government −0.658 (0.584)Largest Party × Single PartyGovt 2.828∗∗∗ (0.566)No-Majority Situation × Largest Party × Single PartyGovt 0.330 (0.593)No-Majority Situation × Minority Government −0.928∗∗∗ (0.299)No-Majority × MinorityGovt × Investiture Vote −0.547∗ (0.293)No-Majority × Minimal Winning Coalition 1.123∗∗∗ (0.264)No-Majority × Number of Parties in Coalition −0.006 (0.119)No-Majority × Median Party in Coalition 0.445∗∗ (0.185)Ideological Range in Coalition −0.610∗∗∗ (0.087)Status Quo 2.169∗∗∗ (0.174)Anti-Establishment Party in Coalition −2.316∗∗∗ (0.352)No-Majority × Second Largest Party 0.348 (0.212)No-Majority × Third Largest Party 1.001∗∗∗ (0.212)Cabinet History 1.331∗∗∗ (0.476)Countries 20Formation Opportunties 352Observations 81,208R2 0.016Max. Possible R2 0.032Log Likelihood −668.841LR Test (df = 15) 1,301.328∗∗∗

Note: New Parsimonious (New_Par) model. Training data. Conditional logit.∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01. Variables that do not vary within choice set canonly enter model via interaction term.

19


metrics for our current purpose. We care, first and foremost, about accurately predicting

which parties will be in government, an important distinction from predicting precisely

which governments will form. If, for example, our model predicts a given coalition and the

true coalition entails the identical composition plus one small surplus party, this is coded

at the coalition-level as a fail. At the party-level, however, all of the predicted parties

would be coded as successes and the extra party not predicted by the model would affect

only the false negative rate. Table C1 in the appendix shows that false positives at the

coalition level more often include most of the actual governing parties than predict a fully

false coalition.

Most importantly, party-level prediction metrics suggest strong predictive perfor-

mance. The out-of-sample column in the party-level ROC plots in Figure 1, for example,

shows that the curve for our parsimonious model run on the data including the single-

party-majority formation opportunities captures 89.5% of the true positive and false

positive area. Thus, for unknown cases, this model detects the government participation

of actual governing parties 89.5% of the time. We therefore feel confident using our par-

simonious model as the basis for modeling parties’ expected probability of government

participation from polling data.

4.3 Step 3: Predicted Values

Previous models were estimated on samples chosen to match those in the literature,

first without and then with single-party governments. Now that we have settled on a

single model – Table 4 (New_Par) – we expand our sample to all available government

formation opportunities for which we have both coalition formation and polling data.

Concretely, this means adding more recent time periods (up to 2018) and more countries

20


Figure 1: Party-level ROC plots. All models as specified in Table 2 and Table 4 respec-tively, estimated on samples including majority situations.

AUC = 0.802

AUC = 0.852

AUC = 0.858

AUC = 0.886

AUC = 0.885

AUC = 0.836

AUC = 0.858

AUC = 0.859

AUC = 0.895

AUC = 0.895

In−Sample Out−Sample

Naive M

odelM

S 2001

MS

2010N

ewN

ew par.

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

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21


(from Central and Eastern Europe). The additional observations, of course, change the

coefficients somewhat, as shown in Table C2 in the online appendix.19,20

We are now able to calculate the CIPs. By plugging values from polls and other

covariates into our New_Par coalition formation model, we can predict the probability

of all possible coalitions. For each party and at each formation opportunity, we can then

sum up the predicted probabilities over all potential governments k of which party q is

part (k = j). More specifically, in its simplest form for any given formation opportunity,

CIPq =K∑k=j

eα′xk∑

k

eα′xk

where α is a vector of coefficients and xk a vector of predictor variables associated with

potential government k.

Our polling data includes an impressive number of political polls but they are not with-

out gaps, and the frequency of polls in different time periods can vary considerably. Both

to smooth out noise and to produce coalition inclusion probabilities at regular intervals,

we average our polling data within months.21In this way, we generate our coalition inclu-

sion probabilities for each party for which polling data are available and that consistently

poll above national electoral thresholds.

Compared to polling data, CIP not only takes account of party characteristics and

coalition inclusion calculus (gross CIP), its conceptualization and computation also al-

low for the calculation of a second variant: any given party’s probability of entering a19A separate restricted model is used for Central and Eastern European countries in which we discard

predictors for single and single-dominant parties to enable convergence.20We test whether each of the final models satisfies the IIA (independence of irrelevant alternatives)

assumption by running each 50 times, each time leaving out all potential governments of a formationopportunity for which a random party that will not participate in the government is included. Wethen compare the coefficients of the full to the restricted model using a Hausman-Test with Bonferronicorrection as suggested by Glasgow, Golder and Golder (2012). We do not find any IIA violations.

21Stochastic uncertainty in the polling data is not a large problem for our purposes for two reasons:(1) we average across all polls within a given month and (2), to be consistent with the approach ofthe coalition formation models on which we build, polling numbers (that proxy seat shares) enter ourcalculation only as binary indicators such as largest party in coalition and minority coalition.

22


government that excludes another party (net CIP). We calculate only one version of net

CIP, one that captures each party’s probability of entering a coalition that excludes the

current prime minister’s (PM) party. For the PM’s party, we use the probability of a

coalition that excludes the largest junior party. Thus, our CIPs allow for the calculation

of theoretically interesting quantities not possible with polling data, vote shares or seat

shares.

5 Coalition inclusion probabilities

5.1 An overview

For simple face validity, Figure 2 presents coalition inclusion probabilities for parties in

three selected democracies that are characterized by differentmodi operandi of government

formation. The box plots depict the distribution of net CIP, i.e. the probability of the

prime minister’s party of being in government without the current junior partner and

likewise, for non-PM parties, the probability of being included in a government excluding

the current PM party. Panel (a) presents the net CIP of Spanish parties from 1980 to

September 2018. Our CIP measure neatly captures and displays the tradition of single-

party governments: either the People’s Alliance Party (PP) or the Socialist Workers

Party (PSOE) (as well as the now defunct Union of the Democratic Centre (UCD)) are

predicted to form governments, even in the absence of potential coalition partners.

Panel (b) displays the same quantities for Swedish parties from 1970 to September

2018. The traditional block-party system, too, shows up in predicted net CIP. While the

Social Democrats (SAP) usually govern alone and are not in need of coalition partners,

the group of conservative parties around the Centre Party (C) and, later on, the Moderate

Coalition Party (MSP) have lower net CIPs, reflecting their lower probability of being

able to form a government without their junior partner in the periods when they were in

government.

23


Figure 2: Distribution of monthly CIP (net) by party across three democracies.

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(c) Germany, 1970-2018

Full party names available in the online appendix.

24


Finally, panel (c) shows net CIP for German parties between 1970 and September

2018. Traditionally, the Free Democrats (FDP) have played the role of the kingmaker,

helping either the Christian Democrats (CDU-CSU) or the Social Democrats (SPD) to

obtain the chancellorship. Each major party on its own, however, has had only a low

probability of forming a government without their junior partner. In summary, for all

three countries and their patterns of coalition formation, net CIP matches expectations.

5.2 Better than polls?

Inclusion in government is a goal shared by most parties, for once in office, even if part of

a coalition, parties have direct access to the levers of policy-making. The probability of

entering government in a multi-party system, however, is considerably more complicated

than attracting popular support. Even the largest government in parliament, if it does

not attain a majority of seats, is not guaranteed inclusion in the government. Inclusion

in the governing coalition most often depends on the availability and electoral fortunes

of potential coalition partners. This “coalition calculus” makes simple polling numbers

inadequate for predicting party behavior and creates the need for an alternative measure

that takes parties’ coalition prospects explicitly into account.

To illustrate this advantage over polls and as a second check of face validity, this time

for gross CIP, we examine one inter-election period in a multi-party country in greater

detail. We compare CIP to polls because they are the only other dynamic measure

of electoral competitiveness that tracks parties between elections, serving as “common

knowledge” about what an election would deliver. Figure 3 plots out both the coalition

inclusion probabilities and the polling numbers for German political parties in the run-up

to the collapse of the Schmidt cabinet in 1982.

The upper panel in Figure 3 shows the predicted gross CIP for four (non-) parliamen-

tary parties, while the lower panel depicts each parties’ support in opinion polls. Two

features strike the eye. First, despite being in opposition, the CDU/CSU enjoyed greater

25


Figure 3: Predicted probabilities to enter government. Schmidt III, 1980-1982.

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The top panel depicts the monthly gross Coalition Inclusion Probabilities for each of the four (non-)parliamentary parties in Germany throughout Schmidt’s third Cabinet. The bottom panel shows voteintention polls for the same parties during the same time period.

inclusion probabilities than the governing SPD for many months before the change in gov-

ernment. Polling numbers show a similar ordering, however, so this is not an advantage.

The second feature, however, does demonstrate the advantage of inclusion probabilities.

The FDP, despite polling uniformly below 10% enjoys a higher CIP than the SPD, which

outpolled the FDP throughout the whole period. These inclusion probabilities highlight

the FDP’s role as “kingmaker”, a small party needed by both large parties to form a

majority coalition. Yet, the FDP loses this pivotal status when the CDU/CSU’s polls

exceed the 50% polling threshold and could form a single-party government.

Finally, the green party B90/Grüne’s CIP is extremely low throughout the whole

period. However, even though they polled above the 5% electoral threshold in 1982, its

26


CIP remained glued to the bottom of the upper panel due to its anti-system and pariah

status, a status the party lost only in the early 1990s.

This example underscores the face validity of our measure and its advantage over the

only other alternative that varies between elections, polls. Variation in parties’ antici-

pation of entering or staying in government between elections is not picked up by more

static measures. As political and policy behavior is likely influenced by parties’ perceived

security, this measure could offer a unique way to predict, for example, the timing of un-

popular reforms (e.g., Hübscher and Sattler, 2017) or opportunistic elections (e.g., Kayser,

2005; Schleiter and Tavits, 2016).

6 Applications

To demonstrate the usefulness of our new CIP measures, we provide two brief applications

to two legislative phenomena central to democratic polities: (1) the role of the opposition

holding the government accountable and (2) the enactment of legislation. Our first appli-

cation considers the introduction of no-confidence motions (NCM) by opposition parties.

As the tabling of NCMs may happen at higher frequencies than country-year observa-

tions would allow for, we model these data at a monthly frequency. Moreover, because

NCMs are often aimed at the prime minister’s party, we use net CIP data. The second

application employs gross CIP data and will show the efficacy of our measure to explain

policy outcomes and their usefulness when aggregated to a yearly level. Both applications

compare CIP to the non-strategic alternative: polls.

6.1 Net CIP: Largest opposition party & no-confidence motions

Table 5 presents discrete-time logit estimation for the occurrence of no-confidence motions

(NCMs). In this estimation we model the likelihood of opposition parties tabling a no-

confidence motion as a function of their chance of building a coalition excluding the

current prime minister’s party. Essentially, we capture whether opposition parties try to

27


bring down coalition governments (our sample is restricted to governments formed by at

least two parties) when their chances of building a new government against the current

PM party in case of an ensuing new election is high. Monthly data on NCMs come

from Williams (2016), which we updated through 2018 by looking into media coverage of

motions of no-confidence.

Next to country and five-year period fixed-effects, we include as control variables the

elapsed share of the constitutional inter-election period (CIEP), the type of coalition, the

number of cabinet parties and the ideological differences between the PM party (PM) and

its junior partner (JP). Central to this estimation are the coefficients of variables capturing

the net CIP of the PM party, the JP and the largest opposition party (LOP). These

variables are introduced with a time-lag to account for the time needed to cognitively

realize the exptected coalition arithmetic were a new election to be held, to attempt to

coordinate with other parties and, finally, to prepare and table a motion of no-confidence.

We compare predictive value of net CIP against those of raw polling data for the same

parties. Additionally, we introduce an interaction between the ideological distance of PM

and JP and JP’s net CIP, i.e. its probability of entering government without the PM

party. We expect that opposition parties are likelier to table a NCM when they sense

that the JP or some parts of the governing coalition might be on board to bring down

or at least disturb an unloved coalition. It is more likely that a junior coalition member

will support a NCM or at least encourage the LOP if its probability of entering a new

government without the current PM is high, a calculation captured by net CIP but less

so by polls.

Table 5 shows two interesting findings. First, it is not the LOP’s polling that predicts

NCMs but rather its potential of forming a coalition excluding the current PM party.

Second, opposition parties seem to take advantage of junior partners’ potential to form

an alternative government when their ideological distance to the PM party is larger. In

other words, when the JP has credible exit options to leave an ideological distant PM,

opposition parties appear to try to drive a wedge between the two. Of course, this does

28


Table 5: Discrete-time logit estimation of no-confidence motions

No-Confidence MotionCIP Polls Interaction CIP Interaction Polls

Share of CIEP Elapsed 0.533 0.077 0.552 0.091(0.492) (0.568) (0.498) (0.558)

Minority Coalition 0.993 1.175 1.110 1.094(0.939) (0.820) (0.914) (0.797)

Surplus Coalition −0.047 0.386 −0.154 0.247(0.502) (0.517) (0.501) (0.538)

Number of Cabinet Parties 0.206 0.004 0.180 −0.053(0.229) (0.243) (0.231) (0.241)

Ideological Distance betw. PM & JP 0.246 0.569 −0.227 0.092(0.333) (0.365) (0.394) (0.553)

CIP (net)t−1, JP −1.836 −6.654∗

(2.507) (3.412)

CIP (net)t−1, LOP 2.101∗ 2.265∗∗

(1.139) (1.101)

CIP (net)t−1, PM 0.654 0.602(0.798) (0.774)

Pollst−1, JP −0.134∗∗∗ −0.161∗∗∗

(0.048) (0.053)

Pollst−1, LOP −0.008 −0.005(0.022) (0.022)

Pollst−1, PM −0.049 −0.048(0.032) (0.031)

Ideol. Distance PM & JP × CIP (net)t−1, JP 3.970∗∗

(1.788)

Ideol. Distance PM & JP × Pollst−1, JP 0.048(0.040)

Constant −6.719∗∗∗ −2.086 −6.517∗∗∗ −1.910(1.042) (2.259) (1.096) (2.200)

Observations 2,382 2,382 2,382 2,382No. of Countries 11 11 11 11No. of Cabinets 100 100 100 100No. of NCM 64 64 64 64Country Fixed-Effects Yes Yes Yes YesLog Likelihood −233.290 −230.288 −231.395 −229.609

Note: Standard Errors clustered by Cabinet in Parentheses; ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01; PM =Prime Minister Party, LOP = Largest Opposition Party, JP = Coalition Junior Partner.

29


not automatically ensure the downfall of a coalition but it will surely disturb its workings

and intra-cabinet trust. Figure 4 plots the marginal effects of ideological distance between

the PM and the JP (0 to 1) on the likelihood of a NCM against the government, across

the whole range of JPs’ net CIP. Unlike polling data, net CIP is a systematic moderator of

the effect of ideological distance on the likelihood of NCMs. Even though NCMs in most

countries are infrequent – only 64 months out of 2,382 saw a NCM – our CIP measure

is still able to pick up some systematic signal from these zero-inflated data.22 Polling

data, too, appears to have some effect on NCM via the JP, but one that runs against

expectations. There is no intuitive explanation why the occurrence of NCMs should be

less likely when the coalition’s junior partner, not the prime minister’s party, polls higher

– in fact the opposite is more likely in case the PM and JP are ideologically distant and

the JP could gain in a new election or cabinet. These findings underscore our confidence

in net CIP as a useful measure of inter-election bargaining leverage.

Figure 4: Marginal Effects on No-Confidence Motion, conditional on CIP

0 0.2 0.4 0.6

0

0.5

1

AME

of Id

eolo

gica

l Dist

ance

(Min

→M

ax)

JP's CIP excl. PM Party

Note: Marginal effect of Ideological Distance on the probability of it tabling a NCM, conditional on JPparty’s CIP. Quantities with 95% confidence intervals obtained from simulations based on the variance-covarance matrix with 1000 random draws. Model 3, Table 5.

22Given the low number of 1s in our data, we have also employed specific models for handling issuesof separation, i.e. Firth’s bias-reduced logistic regression, returning the same results.

30


6.2 Gross CIP: Environmental policy stringency

Having demonstrated the utility of net CIP, we now do the same for gross CIP. We high-

light its usefulness and superiority to polls by modeling a legislative outcome – environ-

mental policy stringency – a composite measure developed by the OECD. The indicator fo-

cuses primarily on air and climate policies by covering policies related to environmentally-

relevant taxes, renewable energy and energy efficiency suppport, performance standards

and information on deposit and refund schemes. It ranges as a continuous measure from

0 to 6, with 6 indicating the most stringent policies (Botta and Kozluk, 2014).23 As this

indicator is measured annually, we aggregate polls, seat shares and the (gross) CIP of par-

ties belonging to the Ecological/Green Party family to the same frequency by calculating

means.

Table 6 presents estimates from linear models with country and period fixed-effects.

A set of control variables captures economic feasibility and environmental necessity for

action – i.e. GDP growth and total green house gas emission per capita – while political

controls account for political feasibility and preference for reform. We control for cabinet

status, the ratification of the Kyoto Protocol as well as the preference for environmental

protection measured by item p501 Environmental Protection: Positive of the Manifesto

Project (Volkens et al., 2015). We measure the cabinet’s level of mean environmental

protection, i.e. the mean of item p501 across all governing parties and also include a

dummy noting the inclusion of a green in the cabinet.

Central to this model is our gross CIP measure that captures the probability of each

country’s green party being included in a new government, were elections to be held. We

compare its predictive performance against two non-strategic proxies for policy-influence,

polls and, less dynamically, seat shares. In all models, whether included separately or

in combination with polls and/or seat share, our CIP indicator predicts environmental

policy stringency. The more that green parties become necessary for prospective coalition23For more information see http://www.oecd.org/economy/greeneco/.

31

http://www.oecd.org/economy/greeneco/


Table 6: Green parties’ influence on environmental policy stringency

Environmental Policy StringencyCIP Polls Seat share CIP & Polls All

(1) (2) (3) (4) (5)

Minority Cabinet 0.059 0.005 0.009 0.055 0.056(0.078) (0.078) (0.076) (0.075) (0.075)

Kyoto Protocol 0.160∗∗ 0.178∗∗∗ 0.193∗∗∗ 0.146∗∗ 0.156∗∗

(0.065) (0.068) (0.067) (0.063) (0.063)

Quarterly GDP Growth (yearly mean) −0.059∗ −0.061∗ −0.060∗ −0.061∗ −0.061∗

(0.033) (0.034) (0.033) (0.031) (0.031)

Cabinet’s Mean Environmental Protection −0.009 0.003 −0.0001 −0.009 −0.011(0.012) (0.011) (0.011) (0.011) (0.011)

Total Greenhouse Gas Emissions/Capita −0.011 −0.014 −0.019 −0.016 −0.019(0.026) (0.026) (0.026) (0.025) (0.024)

Green Party in Government −0.099 −0.023 −0.006 −0.197∗∗ −0.183∗∗

(0.083) (0.081) (0.078) (0.086) (0.089)

Green Party’s Environmental Protection 0.006∗∗∗ 0.007∗∗∗ 0.006∗∗∗ 0.008∗∗∗ 0.008∗∗∗

(0.002) (0.002) (0.002) (0.002) (0.002)

Green Party’s gross CIP (yearly mean) 1.018∗∗∗ 1.315∗∗∗ 1.282∗∗∗

(0.317) (0.307) (0.307)

Green Party’s Polls −1.373 −2.659∗∗∗ −1.846(1.039) (1.028) (1.201)

Green Party’s Seatshare −2.402 −1.485(1.483) (1.812)

Constant 1.647∗∗∗ 1.700∗∗∗ 1.816∗∗∗ 1.921∗∗∗ 1.994∗∗∗

(0.311) (0.276) (0.275) (0.286) (0.275)

Observations 176 176 176 176 176No. of Countries 9 9 9 9 9Country Fixed-Effects YES YES YES YES YESPeriod Fixed-Effects YES YES YES YES YESR2 0.877 0.871 0.872 0.883 0.884

Note: OLS with country and 5-year period fixed-effects. Standard Errors in Parenthe-ses. ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.

32


formation, the greater the current government’s green policy output. These results could

suggest that prime minister parties appeal to or try to subvert green parties by tightening

environmental policy once they become a viable coalition partner or threat. Even when

green parties are in opposition, the PM party has an incentive to court them through

demonstrating policy compatibility.24 In contrast, the coefficients on the variables for

green party polls and seat shares – neither of which capture the strategic arithmetic of

coalition formation – host signs suggesting that they reduce environmental stringency and

neither reaches statistical significance.

7 Conclusion

Political parties are strategic, yet no empirically validated measure exists to capture par-

ties’ incentives to trade off policy against another top priority, government inclusion.

Cabinet parties able to credibly threaten to abandon the current government for an al-

ternative, especially if it would exclude a cabinet policy rival, have high credibility and

bargaining leverage. Likewise, opposition parties that are important to the formation of

future coalitions have policy leverage as well. By estimating and distributing a measure

that captures a quantity central to parties’ strategic calculations and by doing so both

broadly and dynamically – for all relevant parties in 21 countries over multiple decades

at a monthly frequency – we hope that the measures that we provide can enable schol-

ars to investigate a broad swath of new research into a large variety of political and

policy-making behavior.

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Online Appendix

A Missing Polling Data

Sources for supplemental polling data not included in the original Jennings and Wlezien

(2016):

• Austria: Market, Gallup, IMAS, Unique Research, Hajek, OGM, IFES, Karmasin;

www.ots.at, https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_

Austrian_legislative_election

• Czech Republic: Politika! surveys retrieved from the Czech Social Data Archive

(http://archiv.soc.cas.cz/en), Factum, CVVM, STEM, Sanep, Median, ppm,

TNS, TNS Asia, Médea, Phoenix Research; https://en.wikipedia.org/wiki/

Opinion_polling_for_the_Czech_legislative_election,_2017 and respective

sites for earlier elections.

• Denmark: Søren Risbjerg Thomsen’s polling data collection, Epinion, Gallup,

Greens, Norstat, YouGov, Wilke, Voxmeter; https://en.wikipedia.org/wiki/

Opinion_polling_for_the_next_Danish_general_election and respective sites

for earlier elections.

• Estonia: TNS Emor http://www.emor.ee/erakondade-toetus/, TNS Emor, Turu-

uuring; https://en.wikipedia.org/wiki/Estonian_parliamentary_election,

_2019#Opinion_polls and respective sites for earlier elections.

• Finland: Taloustutkimus http://www.taloustutkimus.fi/tuotteet_ja_palvelut/

puolueiden_kannatusarviot/puolueiden_kannatusarviot_2000/, Taloustutkimus,

TNS Gallup; https://en.wikipedia.org/wiki/Opinion_polling_for_the_Finnish_

parliamentary_election,_2019 and respective sites for earlier elections.

39

www.ots.at

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Austrian_legislative_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Austrian_legislative_election

http://archiv.soc.cas.cz/en

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Czech_legislative_election,_2017

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Czech_legislative_election,_2017

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Danish_general_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Danish_general_election

http://www.emor.ee/erakondade-toetus/

https://en.wikipedia.org/wiki/Estonian_parliamentary_election,_2019#Opinion_polls

https://en.wikipedia.org/wiki/Estonian_parliamentary_election,_2019#Opinion_polls

http://www.taloustutkimus.fi/tuotteet_ja_palvelut/puolueiden_kannatusarviot/puolueiden_kannatusarviot_2000/

http://www.taloustutkimus.fi/tuotteet_ja_palvelut/puolueiden_kannatusarviot/puolueiden_kannatusarviot_2000/

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Finnish_parliamentary_election,_2019

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Finnish_parliamentary_election,_2019


• Germany: Forschungsgruppe Wahlen. Allensbach, Emnid, Forsa, GMS, Infrat-

est, INSA, Ipsos; https://en.wikipedia.org/wiki/Opinion_polling_for_the_

next_German_federal_election and respective sites for earlier elections.

• Greece: ALCO, AUEB-STAT, Bridging Europe, Data RC, E-Voice, Focus, GPO,

Kapa Research, MARC, Metrisi, Metron Analysis, MRB, Palmos Analysis, PA-

MAK, PatrisNews, ProRata, Public Issue, Pulse RC, RASS, ToThePoint, VCitizens,

VPRC; https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Greek_

legislative_election and respective sites for earlier elections.

• Hungary: Tárki http://www.tarki.hu/hu/research/elect/index.html, Publi-

cus, Medián, Republikon, Századvég, Iránytü, ZRi, Nézöpont, Tárki, Ipsos; https:

//en.wikipedia.org/wiki/Opinion_polling_for_the_Hungarian_parliamentary_

election,_2018 and respective sites for earlier elections.

• Iceland: MMR, Gallup, Háskóli Íslands, Fréttablðið, Zenter; https://github.

com/gogn-in/polls and https://en.wikipedia.org/wiki/Icelandic_parliamentary_

election,_2017#Opinion_polls and respective sites for earlier elections.

• Ireland: Elections Ireland http://electionsireland.org/polls.cfm?show=table&

year=2016 and earlier years; Red C, Millward Brown, Ipsos, Behaviour and Atti-

tudes; https://en.wikipedia.org/wiki/Next_Irish_general_election#Opinion_

polls and respective sites for earlier elections.

• Japan: NHK http://www.nhk.or.jp/bunken/research/yoron/political/2016.

html and earlier years and Asahi Shimbun http://www.tv-asahi.co.jp/hst/poll/

2016.html and earlier years.

• Netherlands: Nieuw Haags Peil https://home.noties.nl/peil/nieuw-haags-peil/,

Ipsos, De Stemming, Peil, TNS NIPO, I&O Research, Nieuw Haags Peil; https://

en.wikipedia.org/wiki/Opinion_polling_for_the_next_Dutch_general_election

and respective sites for earlier elections.

40

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_German_federal_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_German_federal_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Greek_legislative_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Greek_legislative_election

http://www.tarki.hu/hu/research/elect/index.html

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Hungarian_parliamentary_election,_2018



https://github.com/gogn-in/polls

https://github.com/gogn-in/polls

https://en.wikipedia.org/wiki/Icelandic_parliamentary_election,_2017#Opinion_polls

https://en.wikipedia.org/wiki/Icelandic_parliamentary_election,_2017#Opinion_polls

http://electionsireland.org/polls.cfm?show=table&year=2016

http://electionsireland.org/polls.cfm?show=table&year=2016

https://en.wikipedia.org/wiki/Next_Irish_general_election#Opinion_polls

https://en.wikipedia.org/wiki/Next_Irish_general_election#Opinion_polls

http://www.nhk.or.jp/bunken/research/yoron/political/2016.html

http://www.nhk.or.jp/bunken/research/yoron/political/2016.html

http://www.tv-asahi.co.jp/hst/poll/2016.html

http://www.tv-asahi.co.jp/hst/poll/2016.html

https://home.noties.nl/peil/nieuw-haags-peil/

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Dutch_general_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Dutch_general_election


• New Zealand: Roy Morgan Research http://www.roymorgan.com/findings/

finding-3925-201303050332 and other entries, One News Colmar Brunton, TV3

NFO, NBR-HP Invent, Herald-DigiPoll, 3 News TNS, BRC, Roy Morgan Research,

AC Nielson, https://en.wikipedia.org/wiki/Opinion_polling_for_the_New_

Zealand_general_election,_2017 and respective sites for earlier elections.

• Norway: TNS Gallup Partibarometeret 1964-2010 from Norwegian Centre for Re-

search Data http://www.nsd.uib.no/nsd/english/index.html, Sentio, Opinion

Perduco, Ipsos, TNS Gallup, Norstat, Respons, InFact, Norfakta; https://en.

wikipedia.org/wiki/Opinion_polling_for_the_Norwegian_parliamentary_election,

_2017 and respective sites for earlier elections.

• Poland: CBOS http://www.cbos.pl/SPISKOM.POL/1992/K_107_92.PDF and later

years, CBOS, PBS, TNS OBOP, Demoskop, Pentor, OBW, PBBOUS, PGB, Ip-

sos, GfK Polonia, Homo Homini, SMG/KRC, Estymator, Marcin Palade, PPSP,

WAW, IBRiS, Millward Brown, Dobra Opinia, Arianda, PressMix, PAS-P, Pracow-

nia Mediowa, Kantar Public; https://en.wikipedia.org/wiki/Opinion_polling_

for_the_next_Polish_parliamentary_election and respective sites for earlier

elections.

• Portugal: Eurosondagem, Aximage, Catolica, Marktest, Pitagorica, Intercam-

pus; http://www.popstar.pt/dados.php, Aximage, UCP CESOP, Pitagorica, In-

tercampus, Marktest; https://en.wikipedia.org/wiki/Opinion_polling_for_

the_next_Portuguese_legislative_election and respective sites for earlier elec-

tions.

• Slovakia: Focus http://www.focus-research.sk/?section=show&id=10, Polis,

AKO, Focus; https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_

Slovak_parliamentary_election and respective sites for earlier elections.

41

http://www.roymorgan.com/findings/finding-3925-201303050332

http://www.roymorgan.com/findings/finding-3925-201303050332

https://en.wikipedia.org/wiki/Opinion_polling_for_the_New_Zealand_general_election,_2017

https://en.wikipedia.org/wiki/Opinion_polling_for_the_New_Zealand_general_election,_2017

http://www.nsd.uib.no/nsd/english/index.html

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Norwegian_parliamentary_election,_2017



http://www.cbos.pl/SPISKOM.POL/1992/K_107_92.PDF

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Polish_parliamentary_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Polish_parliamentary_election

http://www.popstar.pt/dados.php

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Portuguese_legislative_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Portuguese_legislative_election

http://www.focus-research.sk/?section=show&id=10

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Slovak_parliamentary_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Slovak_parliamentary_election


• Slovenia: Politbarometer, Slovenia, 1996-2000 Cumulative Dataset https://www.

adp.fdv.uni-lj.si/eng/, Episcentra, RM Plus, Ninamedia, Slovenian Beat, FUDA,

Mediana, UvNG, Delo Stik, SLovenski Utrip, Parsifal; https://en.wikipedia.

org/wiki/Opinion_polling_for_the_next_Slovenian_parliamentary_election

and respective sites for earlier elections.

• Spain: Alef, AP, Append, Aresco, ASEP, Atento STC, Celeste-Tel, CEMOP, CIS,

Citigate Sanchis, Demoiberica, Demometrica, Demoscopia, DYM, ECO, El Pais,

Emopublica, GAD3, Gallup, GESOP, GETS, Gruppo, Iberconsulta, ICP, INE, In-

ner, Intereconomia, Intergallup, Invymark, Ipsos, IO2000, Iope-Etmar, ISIS, Jaime

Miquel & Asociados, La Vanguardia, Metra Seis, Metroscopia, NC Report, Noxa,

Obradoiro de Socioloxia, Opina, OTR, Perfiles, PP, PSOE, Sigma Dos, Simple Log-

ica, Sofemasa, Sondaxe, Tabula-V, TC, Telemarket, Tempo, Typol, Vox Publica;

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Spanish_general_

election and respective sites for earlier elections.

• Sweden: SIFO Barometer (SND 0586-001) from Swedish National Data Service

https://snd.gu.se/en, Skop, Demoskop, Sifo, TEMO, SCB, Gallup, Ruab, Za-

pera, SVT Valu, Synovate Temo, Sentio, Novus, United Mindes, YouGov, Ipsos,

Inizio; https://github.com/MansMeg/SwedishPolls, Sentio, Demoskop, Inizio,

Ipsos, Sifo, YouGov, Novus, SCB; https://en.wikipedia.org/wiki/Opinion_

polling_for_the_Swedish_general_election,_2018 and respective sites for ear-

lier elections.

42

https://www.adp.fdv.uni-lj.si/eng/

https://www.adp.fdv.uni-lj.si/eng/

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Slovenian_parliamentary_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Slovenian_parliamentary_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Spanish_general_election

https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_Spanish_general_election

https://snd.gu.se/en

https://github.com/MansMeg/SwedishPolls

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Swedish_general_election,_2018

https://en.wikipedia.org/wiki/Opinion_polling_for_the_Swedish_general_election,_2018

Coalition

InclusionProbabilities

B Confusion Matrix with Majority Situations.

Table B1: Comparison out of sample: Confusion matrix with majority situations

Naïve Model MS 2001 MS 2010 New New par.not realized realized not realized realized not realized realized not realized realized not realized realized

Coalition Levelnot_realized

19,397 38 19,394 41 19,392 41 19,400 35 19,399 36(0.998) (0.437) (0.998) (0.471) (0.998) (0.471) (0.998) (0.402) (0.998) (0.414)

realized38 49 41 46 41 46 35 52 36 51

(0.002) (0.563) (0.002) (0.529) (0.002) (0.529) (0.002) (0.598) (0.002) (0.586)Precision 0.563 0.529 0.529 0.598 0.0.586Recall 0.563 0.529 0.529 0.598 0.0.586AUPR 0.533 0.57 0.517 0.606 0.61

Party Levelnot_realized

290 67 305 85 305 84 288 50 286 51(0.898) (0.362) (0.944) (0.459) (0.944) (0.454) (0.892) (0.270) (0.885) (0.276)

realized33 118 18 100 18 101 35 135 37 134

(0.102) (0.638) (0.056) (0.541) (0.056) (0.546) (0.108) (0.730) (0.115) (0.724)Precision 0.781 0.847 0.849 0.794 0.784Recall 0.638 0.541 0.546 0.730 0.724AUC 0.836 0.858 0.859 0.895 0.895

Note: All models estimated on a training dataset including single-party majority situations and predictions tested out-of-sample. Column percentages in parentheses. Precision= T P

T P +F P; Recall = T P

P; AUPR = Area under the Precision-Recall Curve; AUC = Area under the Receiver Operator Curve.

43


C Measures of model fit

Table C1: Analysis of Coalition Level Predictions

Naïve Model MS 2001 MS 2010 New New par.False Positives 38 41 41 35 36

Completely false composition 12 5 5 5 4Superset of true coalition 6 8 7 9 8Subset of true coalition 16 22 23 15 17Other 4 6 6 6 7Mean difference of parties in true and predicted coalition 1.769 1.667 1.778 1.667 1.688Predicted rank of true coalitions

1st Rank (= True Positives) 49 46 46 52 512nd Rank 9 11 10 10 73rd Rank 2 3 4 4 54th Rank 4 3 1 3 25th Rank 3 1 4 1 1True coalitions among top 5 predicted coalitions 67 64 65 70 66

Note: Completely false composition indicates no overlap in party composition of true and predicted coalitions;superset of true coalition indidates that predicted coalition is a superset of true coalition; subset of truecoalition indicates that predicted coalition is a subset of true coalition; other indicate that predicted coalitionshas some party composition overlap with true coalition.

At the coalition level, we rely on precision and recall as metrics of model performancebecause the extremely large number of potential coalitions in any given formation oppor-tunity would result in almost perfect prediction of true negatives – as can be seen in theupper-left quadrants in Table B1. Substantively, the use of precision – the share of allpredicted coalitions that are actually true coalitions – reflects our interest in predictingthe single one true coalition and not which coalition out of many has not formed. Recallreports the share of the predicted true coalitions out of all true coalitions. As maximizingeither one of these metrics implies a trade-off, we also report the Area under the Precision- Recall curve (AUPR) at the coalition level in the figures below. At the party level, theabsence of an abundance of true negatives allows us to use the more common Area underthe Curve (AUC) as is seen in Figure 1 in the main text.

44


Figure C1: Coalition-level precision-recall plots. All models, as specified in Table 2 andTable 4 respectively, estimated on samples including majority situations.

AUPR = 0.483

AUPR =

0.589

AUPR = 0.592

AUPR =

0.59

AUPR =

0.602

AUPR = 0.533

AUPR =

0.57

AUPR = 0.571

AUPR =

0.606

AUPR =

0.61


Naive M

odelM

S 2001

MS

2010N

ewN

ew P

ar.

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

Recall

Pre

cisi

on

45


Figure C2: Party-level precision-recall plots. All models, as specified in Table 2 andTable 4 respectively, estimated on samples including majority situations.

AUPR =

0.739

AUPR = 0.808

AUPR =

0.813

AUPR =

0.821

AUPR = 0.823

AUPR =

0.786

AUPR = 0.824

AUPR =

0.827

AUPR =

0.843

AUPR = 0.838


Naive M

odelM

S 2001

MS

2010N

ewN

ew par.

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

0.4

0.6

0.8

1.0

0.4

0.6

0.8

1.0

0.4

0.6

0.8

1.0

0.4

0.6

0.8

1.0

0.4

0.6

0.8

1.0

Recall

Pre

cisi

on

46


Table C2: Final Model Used to Calculate CIP

“Western” Sample CEE(1) (2)

Largest Party in Coalition (LP) 1.156∗∗∗ 1.580∗∗∗

(0.206) (0.266)Single Party Government (SP) −0.938∗∗

(0.420)LP × SP 2.879∗∗∗

(0.411)Majority Situation × LP × SP 0.576

(0.408)No-Majority Situation (NM) × Minority Government (MG) −1.798∗∗∗ −1.350∗∗∗

(0.220) (0.259)NM × MG × Investiture Vote −0.426∗

(0.227)NM × Minimal Winning Coalition 0.869∗∗∗ 1.191∗∗∗

(0.182) (0.209)NM × Number of Parties in Coalition −0.636∗∗∗ −0.552∗∗∗

(0.077) (0.117)NM × Median Party in Coalition 0.653∗∗∗ 0.446∗∗

(0.141) (0.221)Ideological Range in Coalition −0.641∗∗∗ −0.421∗∗∗

(0.063) (0.081)Status Quo 2.692∗∗∗ 2.369∗∗∗

(0.135) (0.270)Cabinet History 0.077 1.858∗∗∗

(0.344) (0.619)Anti-Establishment Party in Coalition −1.828∗∗∗ −0.265

(0.202) (0.304)NM × Second Largest Party 0.728∗∗∗ −0.005

(0.156) (0.219)NM × Third Largest Party 0.998∗∗∗ 0.321

(0.152) (0.205)Countries 20 11Formation Opportunities 616 174Observations 1,102,618 226,203Log Likelihood −1440.931 −613.255

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

47


D Party Names for Figure 2Spain: PP People’s Alliance Party, C-PC Citizens – Party of the Citizenry, CC CanaryCoalition, CDC Democratic Convergence of Catalonia, CDS Democratic and Social Cen-tre, CiU Convergence and Union, EHB Basque Country Unite, ERC Republican Left ofCatalonia, P Podemos, PCE|IU Communist Party|United Left, PNV Basque NationalistParty, PSOE Spanish Socialist Workers Party, UCD Union of the Democratic Centre,UPyD Union, Progress and Democracy.

Sweden: C Centre Party, FP People’s Party, KD Christian Democrats, MP Green Party,MSP Moderate Coalition Party, NyD New Democracy, SAP Social Democrats, SD Swe-den Democrats, V Left Party.

Germany: AfD Alternative for Germany, CDU/CSU Christian Democrats, FDP FreeDemocratic Party, B90/Gr Bündnis 90/Grüne, PDS-Linke The Left/Party of DemocraticSocialism, SPD Social Democrats.

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coalition inclusion probabilitiesmark-kayser.com/papers/kor_coalprobs.pdf · coalition inclusion...

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