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“But one of the weightiest objections to a plurality in the executive…is that it tends to conceal faults and destroy responsibility… The circumstances which may have led to any national miscarriage or misfortune are sometimes so complicated that there are a number of actors who have different degrees and kinds of agency, though we may clearly see upon the whole that there has been mismanagement, yet it may be impracticable to pronounce to whose account the evil which may have been incurred is truly chargeable.” Alexander Hamilton, Federalist no. 70 Introduction The policymaking process in parliamentary democracies often involves “a number of actors who have different degrees and kinds of agency” over policy. Many political scientists have argued, for example, that the party of the prime minister has disproportionate influence on the policy-making process in general ( O’Malley 2007; Diermeier and Feddersen 1998; Huber 1996), but also that partner parties in coalition governments have disproportionate influence in the specific policy areas that are most salient to them (Martin and Vanberg, 2014; Baron and Diermeier, 2001; Bawn and Rosenbluth, 2006), and that opposition as well as government support parties also exert some influence on policy in the legislature (Lijphart, 1999; Strøm, 1998; Hicks and Swank 1992; Jensen and Seeberg 2015). The question we ask in this paper is whether voters have a similar understanding of the policy-making process in complex information environments, or whether power-sharing “tends to conceal faults and destroy responsibility”. The question is not trivial because sensible responsibility attributions allow voters to hold governments accountable for past policy outcomes and to select new governments that are more likely to produce desired policy outputs in the future (Duch and Stevenson, 2008). 1 Furthermore, it is a question that political scientists do not yet know the answer 1 We use the word “sensible” instead of “accurate” to describe normatively desirable attributions of responsibility because it is often impossible to know what the true distribution of policy responsibility is in a given political system. That being said, there are certain variables that political scientists think matter, and we will conclude that voters’
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“But one of the weightiest objections to a plurality in the executive…is that it tends to conceal

faults and destroy responsibility… The circumstances which may have led to any national

miscarriage or misfortune are sometimes so complicated that there are a number of actors who

have different degrees and kinds of agency, though we may clearly see upon the whole that

there has been mismanagement, yet it may be impracticable to pronounce to whose account the

evil which may have been incurred is truly chargeable.”

Alexander Hamilton, Federalist no. 70

Introduction

The policymaking process in parliamentary democracies often involves “a number of actors who

have different degrees and kinds of agency” over policy. Many political scientists have argued, for

example, that the party of the prime minister has disproportionate influence on the policy-making

process in general ( O’Malley 2007; Diermeier and Feddersen 1998; Huber 1996), but also that

partner parties in coalition governments have disproportionate influence in the specific policy areas

that are most salient to them (Martin and Vanberg, 2014; Baron and Diermeier, 2001; Bawn and

Rosenbluth, 2006), and that opposition as well as government support parties also exert some

influence on policy in the legislature (Lijphart, 1999; Strøm, 1998; Hicks and Swank 1992; Jensen

and Seeberg 2015).

The question we ask in this paper is whether voters have a similar understanding of the

policy-making process in complex information environments, or whether power-sharing “tends to

conceal faults and destroy responsibility”. The question is not trivial because sensible responsibility

attributions allow voters to hold governments accountable for past policy outcomes and to select

new governments that are more likely to produce desired policy outputs in the future (Duch and

Stevenson, 2008).1 Furthermore, it is a question that political scientists do not yet know the answer

1 We use the word “sensible” instead of “accurate” to describe normatively desirable attributions of responsibility because it is often impossible to know what the true distribution of policy responsibility is in a given political system. That being said, there are certain variables that political scientists think matter, and we will conclude that voters’

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to. On the one hand, some empirical research suggests that in contexts characterized by a high

degree of power-sharing “responsibility is so blurred that voters should generally find it very

difficult to assess government responsibility” (Powell and Whitten 1993, p. 406). On the other

hand, a different body of research suggests that many citizens in power-sharing contexts vote as if

they understand the distribution of policy influence among political parties quite well (Anderson

1995; Kedar 2005; Duch and Stevenson 2008).

We evaluate between the two contrasting views of voters by first reviewing the literature on

policy influence in order to determine what sensible voter attributions of policy responsibility might

look like. Here we identify several variables that political scientists have argued determine a party’s

policy influence such as roles in the government, party sizes, issue salience and pivotality. We then

rate the variables in terms of how likely we think voters are to correlate them with influence based

on insights from the psychology literature on heuristics and ecological rationality (Gigerenzer and

Gaissmaier 2011; Gigerenzer and Goldstein 2011). Specifically, we argue that voters are more

likely to infer policy influence from a variable that is relatively easy to acquire information about,

and to apply, when their beliefs about relative party influence are formed.

These theoretical possibilities are tested empirically with seven original surveys from five

parliamentary democracies (Denmark, Italy, Germany, the Netherlands, and the UK). These surveys

include direct measures of voter perceptions about the policy responsibility distribution (asking

respondents how much responsibility they perceived that each parliament party had during the most

recent government) and indirect measures of prospective attributions of policy influence in specific

policy areas. For the indirect measures, we first asked respondents which policies they thought

different possible cabinets would pursue if these cabinets were to form after the forthcoming

perceptions of policy influence and responsibility are sensible if they correlate with those variables in the expected ways.

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election. Next, we paired these data with respondents’ perceptions about the policy positions of

each party. With this information we use a statistical model to infer the policy-making influence

that respondents attribute to each party on each policy dimension.

The empirical results illustrate that voters attribute policy responsibility in sensible ways:

First, voters attribute disproportionate responsibility for past policy outputs to the party of the prime

minister within government coalitions and to larger parties within legislative oppositions. Second,

voters assign disproportionate prospective policy weights to the prime minister’s party as well as to

cabinet and government support parties that hold unique positions on issues that are particularly

salient to them. Third, we find evidence that voters take the collaborative history of parties into

consideration when they develop their perceptions about the distribution of influence in plausible

future governments. We thus conclude that voter attributions of responsibility in the policy-making

process are generally sensible because they bear on real influence.2

What determines party influence in power-sharing contexts?

This section identifies the key variables that political scientists have argued determine a party’s

relative influence in the policymaking process. However, before turning to the influence literature it

is necessary to first establish why one would ever expect a systematic relationship between these

variables and voter perceptions of influence. Certainly, it is highly unlikely that a typical voter

knows all of the relevant details that lead to different policy outputs and outcomes. In fact, this lack

of knowledge is a fundamental assumption in some of the most canonical research on representation

(Downs 1957; Powell and Whitten 1993; Powell 2000).

2 Of course, sensible responsibility attributions also require that voters have accurate information about the variables that they use to infer responsibility with (e.g. voters must know what the party of the prime minister is in order to use this variable to infer responsibility sensibly). We provide a detailed empirical analysis of voter information about party characteristics in Appendix B where we conclude that voters also have quite accurate perceptions about the relevant variables on average.

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Yet, work in psychology on ecological rationality pioneered by Gerd Gigerenzer and the

Adaptive Behavior and Cognition (ABC) group at the Max Plank Institute in Berlin (e.g. Gigerenzer

and Gaissmaier 2011; Gigerenzer and Goldstein 2011) shows that citizens often use information

about relevant and easily observable variables to derive at complex cognitions, and there is

emerging evidence that voters do the same when they make political decisions (Duch and Stevenson

2013; Duch, Przepiorka, and Stevenson 2015). It is thus possible that voters use the variables that

we identify below to infer policy influence in a power-sharing context given that they meet a

specific set of criteria. Specifically, the work in the ABC groups suggests that a person will use a

heuristic to make a complex decision when it is “ecologically rational” to do so – that is, when the

heuristic it is cheap, simple to apply, and generally leads to the correct inference. If voters infer

policy influence sensibly, we thus expect that they tend to use heuristic rules that 1) do not require

extensive information search relative to alternative strategies, 2) do not require complex reasoning

to map the information inputs to the inference about influence, and 3) are reasonable accurate.

The variables we identify below all meet the third condition for becoming voter heuristics –

that is, they correlate with real party influence according to political scientists – but they do vary in

terms of how cheap they are to obtain and how simple they are to apply. For example, political

scientists have argued that both the party of the prime minister and the party that occupies the

median ideological position in the legislature exert disproportionate policy influence, but we will

argue that while it is reasonably easy to obtain information about what the party of the prime

minister is, and to link this role to influence, it is more difficult to know what the party of the

ideological median is and to connect this role with influence. In the rest of this section we thus not

only review the variables that political scientists have argued matter for influence, but we also rate

them in terms of how likely voters are to use them as heuristics to infer such influence.

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Parties in government versus parties in the opposition

A key variable that determines a party’s policy influence is whether it is in the government or in the

opposition. In fact, some research leaves no room for opposition parties to shape policy and

assumes instead that government parties have all the power over legislation (Laver and Shepsle

1996). As we will illustrate below, there are other studies that allow opposition parties with some

leeway to take part in the policymaking process, but cabinet parties clearly have some important

advantages. Most importantly, as several political observers have pointed out for more than a

century (Bagehot, 1872; Bryce, 1921; Wheare, 1963; Cox, 1987; Martin and Vanberg, 2011), the

authority to draft legislation has shifted from MPs to cabinet ministers due to the growing need for

technical expertise in an era where the scope of public policy has become very large. Two

observable implications of this trend are that private-member bills now play a much less significant

role in the policymaking process than cabinet sponsored bills (Andeweg and Nijzink 1995: 171),

and that parliamentary policy outputs and outcomes often follow predictable partisan patterns with

more leftist governments being associated with more welfare state expansion during the postwar

economic boom (Cameron 1978; Castles and McKinlay 1979; Hicks and Swank 1992; Korpi 1989),

and less welfare state retrenchment in the “new politics” era of the welfare state (Allan and Scruggs

2004; Korpi and Palme 2003; Jensen and Mortensen 2014).3

Government or opposition status is also a strong candidate for a heuristic that voters might

use to infer responsibility. It is relatively easy to obtain information about which parties are in

government compared to many of the other variables that influence the policymaking process – in

fact, when we asked voters to identify the composition of their current coalition government in the

surveys that we will describe more fully in the empirical section, a majority of our respondents were

3 The “new politics” of the welfare state is a term coined by Pierson (1996) who argued that while a key focus for democratic governments during the postwar economic boom was to claim credit for welfare state expansion, the focus is now on avoiding blame for welfare state retrenchment.

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able to do so in all but one of our seven surveys.4 Furthermore, we expect that it is relatively simple

for voters to connect the government role to policy influence. The first hypothesis of this paper is

thus as follows:

H1: Voters attribute more policy influence to parties in the cabinet than parties in the

opposition

The distribution of influence within the cabinet

While government parties generally have more policy influence than opposition parties, not all

government parties have equal weights in the policymaking process. Rather, parties bargain over

the partisan distribution of government ministries because each minister holds disproportionate

power over a particular portfolio. One ministry is particularly salient in the bargaining process,

namely the prime ministry, and political scientists perceive that this ministry often comes with

important formal powers that give the party that holds it key advantages in the policymaking

process (O’Malley 2007; Rose 1991; King 1994; Lupia and Strøm 1995; Becher and Christiansen

2015; Diermeier and Feddersen 1998; Huber 1996).

There are two formal prime ministerial powers in particular that political scientists have

argued give them disproportionate influence in the policymaking process.5 First, many prime

ministers have the power to dissolve the legislature, and they can use this power as a “bargaining

4 A majority of voters in Italy did not know the identity of the three small partners to the party of the Prime Minister (Partito Democratico). Appendix B shows the percentage of respondents who knew the partisan composition of their government in each sample. 5 Prime ministers in Italy and the Netherlands have neither of these powers, but even in these countries political scientists agree that the party of prime minister has significant influence in the policy-making process (O’Malley, 2007).

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chip” when they negotiate with other parties in the system (Lupia and Strøm 1995: 649).

Accordingly, prime ministers sometimes make dissolution threats to extract policy concessions

from parties that would be electorally disadvantaged by having a new election (Becher and

Christiansen 2015). Second, many prime ministers have the formal power to use the confidence

vote on a particular policy proposal. This allows prime ministers to unilaterally (or together with the

nonpartisan head of state) link the adoption of a bill with the survival of the coalition government.

By doing so, prime ministers can motivate a coalition member to vote with them because the bill is

treated as a vote on who controls floor access in future periods (Diermeier and Feddersen 1998),

and, more generally, confidence vote powers can be used to extract policy concessions from

members of the parliamentary majority (Huber 1996).

We argue that voter information about whether or not a party holds the prime ministry is

another strong candidate for a heuristic that voters might use to infer responsibility. Certainly, this

information is relatively cheap to obtain – At least three thirds of our respondents correctly

identified the party of their prime minister when asked to do so in each of our seven surveys.6

Furthermore, while many voters likely do not understand all the details of dissolution and

confidence vote powers, a prime minister’s influence is often widely publicized in national media,

which makes it easier for voters to map their information about who the prime minister is to

inferences about such influence. The second hypothesis is thus as follows

H2: Voters attribute more policy influence to the party of the prime minister than other parties in

the cabinet

6 Appendix B shows the percentage of respondents who accurately identified the partisan identity of their prime minister in each of the seven surveys.

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Yet, while political scientists perceive that the party of the prime minister has disproportionate

policy influence few would likely argue that this party determines policy outputs unilaterally within

a governing coalition of parties. Rather, several studies have illustrated theoretically and empirically

that policy outputs also depend on a government party’s size operationalized either as cabinet

portfolio shares (Huber and Stephens 2001) and/or as legislative seat shares (Austen-Smith and

Banks 1988; Martin and Vanberg 2014; Grofman 1982).

This distinction between size as a function of seat or cabinet portfolio share is less important

than it may seem as an empirical determinant of influence aggregated across different policy

dimensions. This is because a government party’s share of portfolios is typically proportional to its

share of legislative seats (Gamson 1961; Browne and Frendreis 1980; Bassi 2013) such that the

empirical expectations about policy outputs are the same regardless of whether one operationalizes

government party size in terms of legislative seat or portfolio shares. In specific policy areas,

cabinet ministers have important proposal and information advantages over other policymakers

(Laver and Shepsle 1996), but coalition partners have several institutional tools available to police

the coalition compromise (Thies 2001; Martin and Vanberg 2004, 2005, 2011; Carroll and Cox

2012; Kim and Loewenberg 2005). Accordingly, Martin and Vanberg (2014) have recently shown

that a given ministry’s policy outputs typically reflect the preferences of the entire coalition –

weighted by the legislative seats that each party brings to the government as well as issue salience –

rather than the sole preferences of the party that controls the ministry.

Policy influence is thus correlated with government party sizes in the aggregate regardless

of whether size is conceptualized as portfolio or legislative seat shares, but perhaps more strongly

with seat shares on specific policy dimensions. Consequently, voters may also use map their

perceptions about party sizes onto inferences about such influence. This requires information about

which parties are in government as well as their relative sizes. Clearly, this information is not as

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easy to obtain as information about what the party of the prime minister is, but recent research by

Lin et al. (2017) suggests that voters know the distribution of both government seat and portfolio

shares reasonably well. Furthermore, the cognitive leap from size to influence is likely relatively

straightforward to make – accordingly, Anderson (1995) finds that the effect of economic outcomes

on a party’s vote share is proportional to the party’s size in terms of both portfolio and seat shares.

Our third hypothesis is thus as follows where size is defined broadly such that it can both refer to

seat and portfolio shares:

H3: Voters attribute more policy influence to parties in the cabinet that are larger in size

Finally, several studies have argued that government parties have more influence on issues that are

more salient to them relative to the other parties in the coalition. Martin and Vanberg's (2014) study

on policy outputs, for example, weighs government party positions by issue salience, which is

consistent with Baron and Diermeier's (2001) argument that the coalition compromise on a given

issue dimension will shift toward the ideal point of the party for which the issue is most important.

Likewise, Bawn and Rosenbluth (2006) argue that coalition governments tend to spend more than

single party governments because each coalition party is able to implement their preference for

more spending in the policy areas that are most salient to them. Indeed, even Mudde (2013), who

argues that the general influence of radical right parties has been overstated, acknowledges that

these parties have nonetheless been “catalysts” on immigration policy, which is one of their most

salient issues.

One can also imagine that voters use information about a government party’s issue salience

to infer its influence on that issue. For example, most voters likely understand that green parties

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have intense preferences on environmental policy and that radical right parties have intense

preferences on immigration policy – accordingly, Lin et al . (2017) show that voters use their

perceptions about a government party’s issue salience to make reasonably accurate inferences about

whether that party holds a particular ministry. Furthermore, it seems plausible that voters link their

information input about issue salience to inferences about influence in the government. For

example, it would not be a huge leap for a voter to reach the conclusion that a radical right party has

disproportionate influence on immigration policy in the government because of the importance that

issue has to the party.

H4: Voters attribute more policy influence to government parties on issues that are more salient to

them relative to their partners

The distribution of influence within the legislature

While government parties likely have disproportionate influence on policy outcomes in general, the

possibility remains that opposition parties can influence policy outputs in the legislature as well. In

fact, Lijphart (1999) has argued that consociational systems of governance are preferable to

majoritarian ones precisely because they allow for opposition influence in the policymaking

process. For example, while the power of the legislative committee system varies between countries

(Martin and Vanberg 2011; Powell and Whitten 1993), parliamentary committees are still “widely

recognised to be important arenas of legislative deliberation” (Strøm, 1998, 21). Parties that are not

in government can thus work on committees to shift policy outcomes in a direction they prefer.

Accordingly, there is some empirical evidence that the opposition can, and does, constrain the

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actions of the government using different tactics (Hicks and Swank 1992; Jensen and Seeberg

2015).

It has further been argued that some parties in the legislature are in a more advantageous

bargaining position than others, even if they are in the opposition, namely those that are pivotal to

the government’s agenda. The median legislative party (or median legislator) in particular has been

assumed to exert disproportionate influence due to its pivotal role in the policymaking process

(Baron 1991; Morelli 1999; McDonald and Budge 2005). Laver and Schofield (1990: 111)

summarize this argument pointedly:

The party controlling the median legislator . . . is effectively a dictator on policy . . . . It

makes no difference if it goes off on holiday to Bermuda and sits on the beach getting a

suntan. If we confine ourselves to one-dimensional accounts of coalition bargaining, then

the core position of the party controlling the median legislator implies that its policies

should be enacted whatever it does.

The empirical case for the influence of the legislative median party on policy outcomes is

somewhat weaker, however. On the one hand, McDonald and Budge (2005: 221) find that in terms

of welfare policies, “… the long-run Left-Right position of the parliamentary median provides the

clearest estimate of an effect from political preferences, and those preferences survive controls for

age distributions and the organization of politics along consensual versus majoritarian lines.” On the

other hand, Martin and Vanberg (2014) find “strong evidence that policy lies closer to the coalition

compromise [the seat and salience weighted average of the coalition partners’ policy positons] than

to the ideal point of the legislative median” (p. 994).

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Whatever the true influence of the median legislative party is, we are skeptical that voters

use this variable to infer policy influence. Fortunato, Stevenson, and Vonnahme (2016) do find

evidence that many voters can order parties on the left-right policy dimension in a consistent way,

but we suspect that it may require too complex reasoning to map this information to an inference

about influence. Specifically, while there is experimental evidence that citizens understand and act

on pivotality (Bartling, Fischbacher, and Schudy 2015), we suspect that most voters simply do not

know what a median party is, or why it is potentially powerful, and thus are unlikely to link this role

to influence. Yet, despite our skepticism we do want to test this possibility because of the attention

the median legislative party has received among political scientists, and so our fifth hypothesis is as

follows:

H5: Voters attribute more policy influence to the median party in the legislature than other parties

in the legislature

However, we need not think of the median party as the only party that is pivotal to the

government’s agenda in the legislature. Rather, minority governments must sometimes rely on other

parties in the legislature to support them on investiture votes and votes of no confidence. Such

support parties may thus exert disproportionate influence because they are pivotal to the

government’s continued existence. For example, Strøm (1984) argues that minority governments

form because some (support) parties anticipate that they can influence policy from outside the

cabinet while avoiding electoral responsibility for undesirable outcomes. Furthermore, support

parties themselves frequently highlight the potential influence that comes with their role. In the

lead-up to the 2015 Danish election, for example, the leader of the Danish People’s Party justified

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their strategy to seek a support party role precisely in terms of the influence that this role comes

with: “In our assessment, we will not gain the biggest influence by participating in a government...

but as a hopefully strong support party for the new government” (Politiken, 2014).

While government support parties may have disproportionate policy influence in general,

there are contrasting views about whether voters use the support party role to infer such influence.

On the one hand, Strøm clearly assumes (but does not test) that voters do not recognize the

influence that the support party role comes with, and thus do not hold support parties accountable.

On the other hand, Tromborg et al. (2017) have shown that most voters in a minority government

context can correctly identify the support parties in their system, indicating that it is not too difficult

for voters to obtain information about who the support parties are, and that voters also

retrospectively attribute support parties disproportionate responsibility for past policy outcomes in

certain contexts, indicating that voters may be able to map their information inputs about support

parties onto inferences about policy influence. The final hypothesis we test in this paper is thus as

follows:

H6: Voters attribute more policy influence to support parties for minority governments than other

parties in the legislature

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Which attributional rules do voters use to infer policy influence?

The candidate heuristics we identified in the previous section may allow voters to infer

responsibility for policy outcomes in general and in specific policy areas. To test these possibilities

we present two separate empirical subsections. The first section analyzes whether voters use a

party’s government role, size and ideological centrality to retrospectively infer its responsibility for

past policy outcomes in general. In the second in subsection we test whether voters attribute

influence sensibly when they form their expectations about prospective governments using an

indirect measure of perceptions of influence in specific policy areas. This latter analysis not only

complements the first, but it also allows us to examine whether parties are perceived to influence

policy disproportionately in the areas that are most salient to them, and to examine the relationship

between support party status and perceived policy influence, which we do not have sufficient data

to explore in the first section.

How do voters form their perceptions about policy responsibility retrospectively?

The analysis in this first empirical subsection relies on five original surveys designed by our

research team and implemented by Survey Sampling International (SSI).7 These were conducted in

2014 in Denmark, Germany, and Italy, and in 2012 in the United Kingdom and the Netherlands.8

These cases were chosen because each had an incumbent coalition cabinet, and while our main

empirical goal is not a cross-national comparison (we only have five countries) these cases also

have some interesting variation in power-sharing institutions and other government characteristics

(e.g. majority governments in Italy, Germany and the United Kingdom and minority governments in

7 SSI’s sampling procedure is described in more detail in appendix A 8 The survey in the Netherlands was implemented by YouGov, which uses a sampling procedure that is similar to that of SSI.

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Denmark and the Netherlands). The relevant characteristics of the parties in the five countries are

summarized in Figure 1.

Figure 1: True party characteristics in the empirical sample.

In order to test the various hypotheses with this sample of countries and parties we needed to

measure, among other things, respondents’ perceptions of each party’s role in the government

and/or the opposition, their perceptions of each party’s legislative size, and the relative amount of

policy-making influence they attribute to each. Consequently, we collected this information for all

major and most minor parties in each country.9 No previous work of which we are aware has

9 The names of the parties involved in each of the surveys are presented in Appendix A.

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attempted to directly measure voters’ attributions of general policy-making responsibility among

parties.10 Thus, our new measure of this concept pays careful attention to the way the concept is

defined and used in the theoretical literature we explore. Specifically, the theoretical concept we

wish to measure is not about one specific means of policy influence, but general influence. Thus,

we built a question that encourages respondents to think about all the various ways that parties

might influence policy outcomes whether these are formal mechanisms (like votes) or informal (like

private persuasion or even “back-room” payoffs).

We also wanted an aggregate measure of responsibility for policy outcomes across all of the

different policy domains on which governments and legislatures take action. Thus, we asked

respondents about their views on responsibility for all policy outcomes over a specific period of

time (the life of the current government). Finally, our theoretical concerns explicitly equate policy-

making responsibility with perceptions of influence over policy outcomes and not broader notions

of responsibility that might work through other mechanisms (e.g., emotional responses).

Consequently, we couched the question in terms of “influence” rather than the word

“responsibility.”

The “legislative process” consists of legislators proposing, modifying, and

voting on legislation. Ultimately, this process produces a set of new laws

and modifications to old laws. Taking into account of all the various

means parties may use to influence the legislative process, how much

influence do you think each of the parties below ultimately had on the

outcomes of the legislative process in [NAME OF COUNTRY] during the

most recent government?

10 Other surveys have asked respondents to attribute responsibility to different levels of government (Caplan et al., 2013; Johns, 2011; Léon, 2011; Hobolt and Tilley, 2014) but not to different parties.

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Respondents were then asked to place each party on a 1-5 scale, where a “1” corresponded to “No

influence at all” and a “5” corresponded to “A lot of influence.”11 The dependent variable in all of

our empirical models in this subsection is thus the respondent’s answer to this survey item for each

party.

In order to explore the sources of these attributions, we also needed to measure respondents’

perceptions of party characteristics. We did this by asking respondents what percentage of

legislative seats they thought that each party held, whether each party was the party of the prime

minister, a cabinet partner, in the opposition, or without legislative seats, and what the ideological

left-right position of each party was (the specific question formats as well as summary statistics are

included in appendix A). In the remainder of this section, we first explore which (if any) of these

cues voters use to assign policy-making responsibility to parties. To do so, we set up the data so that

the unit of analysis is a “party-respondent” and the dependent variable is the respondent’s

perception of a given party’s level of policy-making influence. The independent variables measure

the respondent’s perceptions of this party’s characteristics (e.g., sizes, roles, and ideological

positons). These data allow us to empirically examine whether voters use cues based on party sizes

and roles to infer relative levels of policy-making influence among parties.

We begin our empirical analysis of retrospective responsibility attributions with a set of

simple graphs that plot our respondents’ retrospective attributions of policy-making influence

against perceived party roles and sizes.12 Do voters attribute disproportionate influence to parties in

the government in general, and to the party of the prime minister in particular? Do they attribute

11The survey in the United Kingdom used a different scale for the dependent variable (a “1” to “6” scale instead of a “1” to “5” scale. To make comparison meaningful we therefore recode the dependent variable in the United Kingdom so that a 6 “complete influence” is coded as a 5 “A great deal of influence”. The exact question wording for the United Kingdom is presented in appendix A. 12 We did not give respondents a support party role option (except for a small subsample in Denmark). Consequently, we explore the relationship between the support party role and perceived policy influence in more detail in the next subsection where we ask respondents what policies they thought would be pursued in different hypothetical governments with different support parties.

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more responsibility to parties that they perceive hold more legislative seats? If so, then we can

reject the idea that voters’ response to power sharing is an inability to attribute responsibility

sensibly (as long as voters also have reasonably accurate information about the party characteristics,

which we show that they do in Appendix B).

Figure 2 gives our respondents’ average assessment of policy-making responsibility for

parties of different perceived legislative sizes. The red dots correspond to the perceived legislative

seat share of a party on the x-axis, and to the average level of responsibility that our respondents

attributed to parties that they assigned to a given role (PM, partner or opposition) on the vertical

axis. The blue bars represent 95 percent confidence intervals.13 The histogram at the bottom of each

panel is the empirical distribution of perceived party sizes in the relevant sample, with black dots

indicating the true sizes of the parties that fit into the category.

13 These values (and their 95 percent confidence intervals) were derived from coefficients that were obtained by regressing policymaking influence on seat share dummy variables for various seat share intervals (e.g. a dummy variable that takes a “1” for all observations where a respondent perceived the party to have between 10 and 15 percent of the legislative seat share, and “0” otherwise).

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Figure 2: Perceived party characteristics and responsibility attribution

Note: Red dots are the average responsibility attributed to a perceived party type. Blue vertical lines are 95 percent confidence intervals. Orange vertical lines show the distribution of sample responses. The black dots on the bottom are true party sizes for the different parties in the parliament. The number of observations is 844 in Denmark, 797 in Italy, 856 in Germany, 805 in the Netherlands, and 774 in the UK.

The first insight we can glean from Figure 2 is that there is evidence for the hypothesis that

voters attribute more responsibility to parties they perceive are in government than parties they

perceive to be in the opposition (H1). This can be seen in the responsibility attribution shift on the

vertical axis between parties perceived to be in the opposition versus parties perceived to have a

government role (PM or partner) at a given perceived size. Furthermore, there is evidence in favor

of both the hypothesis that that there is an additional attribution bonus for holding the Prime

Ministry (H2), and that attributions of policy making influence for government are proportional to

party size (H3). The former is seen in the level shift in attributions between the PM and partner

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panels (at a constant perceived size level), and the latter is seen in the positive relationship between

perceived legislative share and attributed influence (at a constant role).

Importantly, however, our respondents do not on average assign “no influence” to

opposition parties (which was the lowest option – coded 1 -- on our scale), and certainly do not

assign this value for all seat shares. Instead, our respondents seem to think that opposition parties

can exert at least some influence (a “2” on our scale was labeled “very little influence” and a “3”

was labeled “some influence”) on policy. Further, the patterns in Figure 2 reveal that the functional

relationship between legislative seat share and attributions of influence (i.e., the slope of the lines)

is very similar across different government and opposition roles: While the lines in the figure are

shifted up and down for each role, the shapes are much the same. This is exactly the pattern one

would suspect if voters mix a simple proportional legislative seat share heuristic with one that gives

“bonuses” at every level of seats to cabinet parties (with a bonus for being in government generally,

and a larger bonus for being the party of the prime minister specifically). This heuristic only

requires voters to know the legislative seat sizes of the parties, and it is sensible in the sense that

larger opposition parties may, for example, exert more influence on policy outputs in legislative

committees (Strøm, 1998).

The non-parametric relationships between roles and party size depicted in these two figures

quite clearly support the notion that voters are sensible in their retrospective policymaking

attributions in each of the countries in our sample. Further, they are consistent with what we would

expect if voters are using simple cues that rely only on knowledge of legislative seat shares and

party roles in the government and opposition. However, these figures do not allow us to explore the

fifth heuristic we introduced above in which voters give a disproportionate share of policy influence

to median parties. Furthermore, in order to know whether voters are really using heuristics rather

than reporting direct knowledge of policy influence, it is necessary to demonstrate that the

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relationships between perceived party characteristics and attributions of influence that are apparent

in Figure 2 persist when we control for the parties’ true levels of policy influence. If this is not the

case, it suggests that voters may not be applying heuristics to produce the results we see. Instead, it

could simply be that true differences in party sizes and roles cause real differences in policy

influence across parties and these differences in influence are directly observed by voters (via, for

example, media reports). If, on the other hand, the relationship between perceived party

characteristics and responsibility attribution persists after controlling for true party characteristics

then at least some of our respondents must be acting consistently with the heuristic rules, even

though they are applying them to incorrect inputs (i.e., mistaken perceptions of party roles and

sizes).

Thus, we estimate a series of ordered probit models (one for each country) in which the

dependent variable is the five-category measure of attributed policy-making influence described

above with the unit of analysis being the respondent-party. We include covariates in the model to

capture the main hypotheses above: A “Prime minister” dummy variable that takes a “1” for the

party the respondent perceived to hold the prime ministry and “0” otherwise; a “cabinet partner”

dummy variable that takes a “1” for the parties the respondent perceived to be coalition partners and

“0” otherwise; an “opposition party” dummy variable that takes a “1” for the parties the respondent

perceived to be in the opposition and “0” otherwise; and perceived seat and portfolio variables. The

omitted category for the party role dummy variables is “no seats in parliament”.

The models also include a variable that measures parties perceived party sizes as well as a

squared term to account for the bend in the slope that we observed in Figure 2. Furthermore, the

models include two measures that capture the general idea that voters may attribute greater

responsibility to more moderate parties in general and to median parties in particular (H5).

Specifically, we calculate each respondent’s perceived median party using respondents’ placements

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of the parties on the left-right scale.14 In addition, we calculate the perceived ideological

“centrality” of each party as the party’s perceived ideological distance from the perceived median

party.

We control for true policy influence by including a set of dummy variables in the model for

each party. The estimates on these dummy variables capture all the influences on attributions of

responsibility associated with each party that are common to all respondents and due to unmeasured

variables associated with each party. This includes any influence that true levels of influence might

have on perceived influence, independent of perceived party sizes and roles (and the other measured

variables in the model).

Finally, it is important to keep in mind that there are multiple rows for each individual. This

data structure violates the assumption that the observations are independently distributed if some

individuals view the responsibility attribution scale differently than others. For instance, it is

possible that some individuals give a different meaning to “a great deal of influence” than other

individuals. To help reduce this concern we estimate all models with random intercepts for

respondents. The regression coefficients from this model specification are shown in Table 1.

14 We calculated this variable such that there can be only one median party for each respondent, but allowing for multiple median parties does not change our conclusions.

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Table 1: perceived party characteristics and responsibility attribution holding true characteristics constant

Parameter Denmark Italy Germany Netherlands UK

Prime minister 1.862*** 1.418*** 2.060*** 1.750*** 1.621*** (0.16) (0.11) (0.14) (0.11) (0.14) Cabinet partner 1.484*** 0.861*** 1.224*** 1.437*** 1.041*** (0.11) (0.06) (0.08) (0.08) (0.12) Opposition 0.732*** 0.425*** 0.833*** 0.658*** 0.414*** (0.10) (0.05) (0.06) (0.07) (0.10) Seats 0.059*** 0.060*** 0.070*** 0.047*** 0.043*** (0.00) (0.00) (0.00) (0.01) (0.00) Seats² -0.001*** -0.000*** -0.001*** -0.000** -0.000*** (0.00) (0.00) (0.00) (0.00) (0.00) Median party 0.053 0.068 0.091 -0.051 -0.033 (0.05) (0.05) (0.05) (0.04) (0.06) Centrality 0.005 0.002 -0.006 -0.013 0.061** (0.01) (0.01) (0.02) (0.01) (0.02) Party 1 -0.173** 1.457*** -1.935*** -0.238* 1.507*** (0.06) (0.08) (0.11) (0.09) (0.14) Party 2 -0.646*** -0.009 -0.116 -1.252*** -0.471*** (0.08) (0.07) (0.13) (0.10) (0.07) Party 3 1.017*** -0.311*** -0.985*** -1.155*** 0.429*** (0.09) (0.07) (0.08) (0.10) (0.09) Party 4 -0.344*** 0.537*** -1.356*** -1.382*** 0.845*** (0.08) (0.07) (0.09) (0.10) (0.10) Party 5 -1.947*** 0.699*** -1.518*** -1.070*** -0.360*** (0.12) (0.07) (0.10) (0.09) (0.08) Party 6 -1.006*** 0.766*** -1.936*** -1.882*** - (0.08) (0.07) (0.11) (0.11) Party 7 0.581*** 1.404*** - -0.299** - (0.14) (0.12) (0.09) Party 8 -0.267*** -0.087 - -1.380*** - (0.07) (0.07) (0.10) Party 9 - 0.065 - -1.310*** - (0.07) (0.11) Cut point 1 -0.675*** 0.145* -1.255*** -1.502*** -0.587*** (0.13) (0.07) (0.11) (0.13) (0.10) Cut point 2 0.758*** 1.311*** 0.175 -0.123 0.937*** (0.13) (0.07) (0.11) (0.13) (0.10) Cut point 3 1.906*** 2.359*** 1.554*** 1.062*** 2.102*** (0.13) (0.07) (0.11) (0.13) (0.11) Cut point 4 3.062*** 3.539*** 2.918*** 2.291*** 3.231*** (0.13) (0.08) (0.11) (0.13) (0.12) Random intercept variance:

0.282*** 0.519*** 0.476*** 0.411*** 0.649***

Individuals (0.03) (0.04) (0.04) (0.03) (0.06) Obs. 5,576 6,598 5,555 7,003 3,689

***p<.001, **p<.01, *p<.05, two-tailed test. All coefficient estimates are derived using an ordered probit estimator. Party 1 = DK: Dansk Folkeparti; IT: FI-PdL; GE: AfD; NL: CDA; UK: Conservatives Party 2 = DK: Det Konservative Folkeparti; IT: FdI; GE: CDU/CSU; NL: CU; UK: Greens Party 3 = DK: Det Radikale Venstre; IT: IdV; GE: Die Grünen; NL: D66; UK: Labour Party 4 = DK: Enhedslisten; IT: LN; GE: Die Linke; NL: GL; UK: LDP Party 5 = DK: Kristendemokraterne; IT: M5S; GE: FDP; NL: PvdA; UK: PC Party 6 = DK: Liberal Alliance; IT: NCD; GE: Piraten; NL: PvdD; UK: SNP Party 7 = DK: Socialdemokraterne; IT: PD; GE: SPD; NL: PvdV; Party 8 = DK: Socialistisk Folkeparti; IT: SC; NL: SP; UK: UKIP Party 9 = DK: Venstre; IT: SEL; NL: SGP; Party 10 = IT: UdC; NL: VVD

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The main message from Table 1 is simply that all of our early conclusions from Figures 2

hold in this multivariate model. In every country, all the role and seat variables are statistically

significant, in the right direction, and statistically different from one another in expected ways (i.e.,

the coefficients on the PM, partner, and opposition dummy variables). In contrast to this, there is

essentially no support that respondents’ attributions of policymaking influence are conditioned on

the identity of their perceived median party or the perceived ideological centrality of any party. For

example, in Denmark, the estimated coefficient on the perceived median party dummy variable is

35 times smaller than the coefficient on the perceived PM dummy. Apparently, our respondents do

not associate policy influence with ideological moderation. This result is very much in keeping

with our expectations based on the relative costs of collecting ideological information about all the

parties as well as the difficulty many voters likely have mapping this information input to the

inference about influence.

Overall, the results presented above suggest that voters in complex coalitional systems attribute

policy influence in a sensible way and that they form these attributions by leveraging two easily

observable party characteristics – legislative seat shares and roles in the government. The next

subsection explores whether voters also attribute policy influence sensibly in specific policy areas.

Prospective Expectations about Policy Influence for Specific Policies.

In this subsection, we examine voter attributions of policy making influence in a different way that

not only adds nuance to the results reported in the last section, but also allows us to examine

different attributional dimensions that were not possible to analyze with the general measure of

policy influence used above. Specifically, we rely on data from two additional surveys that we

conducted in the week before the 2015 elections in the UK and Denmark to attempt to measure

respondents’ expectations about which policies different potential cabinets would pursue if they

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were to form after the election.15 By pairing these data with respondents perceptions of the policy

positions of each party included in the potential cabinet, we can estimate the policy making

influence that each respondent expects each party in the new coalition to exert – expectations which

we can then compare with various candidate heuristics. In addition, since we asked respondents

about a number of different policies, we can explore how (and why) expected influence varies by

policy domain.

In both surveys, we included questions asking respondents to place all the contesting parties

on three different (seven point) policy scales. Two of these scales were the same in both countries:

1) taxes and social spending, and 2) integration in the EU. The third differed across countries: For

the UK, it concerned Scottish independence, while for Demark it concerned asylum for refugees

(see appendix A for the exact questions and answer categories). After placing parties on these three

policy dimensions, respondents were (much later in the survey) presented with a series of

hypothetical cabinets and asked which policy positions they expected each cabinet to pursue. For

example, in the UK survey, the question preamble and question for one example cabinet was:

15 These surveys were nationally representative internet samples for the UK and Denmark respectively. They were administered by SSI international in the week before each election. Summary statistics for these surveys are presented in Appendix A.

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Now, we are interested in your opinion about the kinds of policies you think would result if

different combinations of parties were to form a cabinet.

Below, we describe three policy issues. Please indicate the policies that you think the new

government would pursue if it was supported by the following parties (whom together

controlled a majority of seats in the House of Commons):

Prime Minister: Labour

Cabinet Partner: The Scottish National Party

This was followed by the same three policy scales on which respondents had previously placed the

parties. Further, in some cases, in addition to (or rather than) a cabinet partner, we described a

support party that would not lead a government ministry but would support the party of the Prime

Minister on votes of confidence. The full set of hypothetical coalitions about which respondents

were asked are listed in the top row of Tables 3-5 and 7-9 for the United Kingdom and Denmark,

respectively.

Our primary goal in analyzing these data is to get an estimate of the implied policy influence

that the average respondent expects each government party to exert in each policy domain. The data

we work with are the respondents’ expected coalition policies for each hypothetical coalition and

their perceived positions of each party on those same policy dimensions. Thus, we want to find the

mapping between these perceived policy positions and the coalition policy that best fits the data

across respondents. To do this, we execute the following strategy:

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1. Let party i be a member of hypothetical cabinet G and a respondent’s perceived policy

position for party i on policy dimension X be xi.

2. Choose an arbitrary set of non-negative weights that sum to one over the parties in G and

call the weight for party i i.

3. Calculate 𝑋𝐺 = ∑ 𝛼𝑖𝑥𝑖𝑖∈𝐺 , which is the weighted average of the perceived positions of the

cabinet partners given the arbitrary weights.

4. Calculate this weighted average for each respondent in the sample and store it in the data

set.

5. Regress this variable on the expected policy positions of the hypothetical coalition reported

by respondents. The r-squared of this regression is a measure of how well the weighted

average policy positions using the arbitrary weight predicts respondents’ expectations about

the coalition policy.

6. Repeat steps 2-5 for every possible combination of weights (or a large sampling over the

entire support of these weights) and find the set of weights that produce the best fit (the

highest r-squared).

The set of best fitting weights for each hypothetical coalition and each policy domain is a measure

of the implied policy influence that the average respondent gives to each party in the hypothetical

coalition for that policy dimension. Below we simply call this the “expected policy influence.”16

16 This exercise produces an r-squared for each combination of weights examined and so we can explore how the fit of the models change as the weights assigned to different parties’ policy positions change. Reassuringly, the r-squared statistic for all cases was a smooth function of the weights with a single global maximum.

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Analysis with data from the United Kingdom

Tables 3-5 give the result of this exercise for each of the three policy domains about which we

asked in the 2015 UK survey. The top number in each cell is our estimate of the expected policy

influence of each party in each of five hypothetical governments. In addition, each table provides, in

the first column, the average share of legislative seats that the average respondents expected the

party to win in the upcoming election.17

Table 2: Taxation and spending

Party Avg. expected seat share

PM: Labour Partner: SNP Support: None

PM: Labour Partner: LDP Support: None

PM: Labour Partner: None Support: SNP

PM: Conservative Partner: LDP Support: None

PM: Conservative Partner: LDP Support: UKIP

Labour 34 60 46 67 0 0 LDP 8 8 31 4 7 7 Conservatives 36 0 0 0 81 75 UKIP 6 0 0 0 11 17 SNP 6 32 23 29 1 1

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 748.

Looking first at the implied weights for tax policy, several results are clear. First, voters do not

perceive that opposition parties exert much (if any) influence on the policies that governments

pursue regardless of their size. This may seem like it contrasts our findings from earlier, but recall

that our earlier question asked about retrospective influence in the policy-making process whereas

the question used for this analysis infers a party’s prospective influence on the policies that the

government pursues. Clearly, it is possible for opposition parties to influence the policymaking

process (e.g. in the committees or in “backroom” deals) without influencing the policies that

governments pursue (e.g. in the cabinets), and the results presented here suggest that voters

understand this distinction.

17 The question asked respondents specifically about how large they thought that each party in the system would be after the election. The specific question wording is presented in Appendix A.

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Second, respondents’ expect that the party of the prime minister will have much more

influence than its partners regardless of the hypothetical government that we presented voters with.

Concretely, Labour’s expected policy influence is a minimum of 46 percent and a maximum of 67

percent when we gave it a prime minister role while its assigned partners expected policy influence

is at a maximum of 32 percent. This difference is even starker in hypothetical governments led by

the Conservatives, which are attributed a minimum of 75 percent influence. To be sure, it is not

possible for us to disentangle whether voters attribute expected policy influence in this way due to

the ’prime minister heuristic’ (H2) or the ‘large party in government heuristic’ (H3) because we did

not specify the distribution of seat shares in the party system.18 Yet, the attributions of influence to

these parties are clearly sensible given what political scientists know about the true influence that

large prime minister parties have on policy.

Third, voters attribute much more responsibility to government support parties than regular

opposition parties (H6). In fact, the levels of responsibility attributed to support parties are

comparable to those of partner parties. This can be clearly seen by comparing policy influence

attributed to the SNP as a partner (32 percent) and as a support party (29 percent) to the same

government led by Labour. In fact, responsibility attributed to UKIP as a support partner is higher

than responsibility attributed to LDP as a coalition partner in the same Conservative led

government, though this finding is likely partially due to voters taking into consideration the recent

history of the incumbent Conservative-LDP government. We explore this and other possibilities in

more detail below.

18 We cannot use the expected party size question from earlier in the survey for this purpose because we are imposing an external assumption about what the distribution of party seats looks like when we propose a given coalition (i.e. that the government and support parties together comprise at least 50 percent of the seat share), and this assumption often contradicts voter expectations about the party specific outcomes of the election.

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Table 3: Scottish Independence

Party Avg. expected seat share

PM: Labour Partner: SNP Support: None

PM: Labour Partner: LDP Support: None

PM: Labour Partner: None Support: SNP

PM: Conservative Partner: LDP Support: None

PM: Conservative Partner: LDP Support: UKIP

Labour 34 36 54 44 0 7 LDP 8 8 25 11 34 8 Conservatives 36 0 12 0 52 52 UKIP 6 7 8 7 13 32 SNP 6 49 10 38 1 1

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 748.

We have yet to test one hypothesis both of our empirical subsections, namely that issue

salience matters in the government (H4). In order to do that we need to compare influence

attributions across multiple policy dimensions. Consequently, Tables 4 and 5 show voter policy

weights on the issues of Scottish independence and EU integration, respectively. The former issue is

almost definitional for the SNP and the latter is almost definitional for UKIP. Accordingly, SNP is

perceived by voters to have greater influence on the issue of Scottish independence than any other

policy dimension and UKIP is perceived to have greater influence on the issue of EU integration

than any other policy dimension. Indeed, for the Labour-SNP government, respondents expect SNP

to have greater influence on policy than the Labour prime minister (49 percent to 36 percent).

Likewise, in Table 4 UKIP’s influence as a support party is perceived to be almost the same as that

of a conservative prime minister on the issue of EU integration (48 percent to 51 percent). This

suggests that many voters are aware of the long-term policy reputations or images of the parties and

use that information when they develop their perceptions about the distribution of policy influence.

Table 4: European Union

Party Avg. expected seat share

PM: Labour Partner: SNP Support: None

PM: Labour Partner: LDP Support: None

PM: Labour Partner: None Support: SNP

PM: Conservative Partner: LDP Support: None

PM: Conservative Partner: LDP Support: UKIP

Labour 34 66 53 64 0 0 LDP 8 0 30 0 1 0 Conservatives 36 0 0 0 81 51 UKIP 6 0 0 0 17 48 SNP 6 34 17 36 1 1

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 748.

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Finally, as we alluded to earlier, the results from the United Kingdom are also indicative that many

voters take into consideration the historical record when they develop their prospective perceptions

of party influence. Specifically, we assigned the LDP to a partner role in a government led by

Labour and to two partner roles in a government led by the Conservatives (with one of them

including UKIP as a support party). The results show that the LDP was attributed a lot more

influence in a government with Labour than a government with the Conservatives (except on the

issue of Scottish independence with no support parties). This is interesting because our survey was

implemented at the end of a Conservative-LDP government where the LDP arguably had

demonstrated weak influence, which was epitomized in the coalition government raising tuition fees

despite the LDP making an explicit campaign promise to do the opposite. In fact, according to the

party leadership it was precisely these events that eventually caused the disappointing election

outcome for the party (the LDP went from having 57 to 8 seats in the House of Commons).19 The

results presented in Tables 3-5 thus not only show evidence that voters use heuristics to infer policy

influence, but also that they use political news and history to attribute a party’s influence sensibly.

We will explore both possibilities further using the survey data from Denmark.

Analysis with data from the United Kingdom

Unlike in the United Kingdom, coalition governments are the norm in Denmark because the Danish

system is characterized by a high degree of power sharing both in terms of its proportional electoral

rules and the inclusiveness of the committee system. Accordingly, the incumbent minority

government in the 2015 election was a center-left coalition between the Social Democrats and the

Radicals, supported by two leftist parties, namely the Unity List and the Socialist People’s Party.

The Danish case thus allows us to test whether voters attribute parties policy influence differently in

a system that is traditionally (and presently) characterized by coalition governments and other

19 https://www.theguardian.com/politics/2015/may/12/nick-clegg-university-tuition-fees-norman-lamb

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power sharing institutions. The 10 parties competing in the 2015 Danish general election are

presented in Table 5 (the parties are ordered from the ideological left to the ideological right).

Table 5: The distribution of Danish political parties in 2015

Party Party group Role in incumbent government

Unity List Communists/Greens Support Party

Socialist People’s Party Socialists Support Party

The alternative Postmaterialists/Greens No seats in parliament (first election)

The Social Democrats Social Democrats Prime minister

The Radicals Liberals (center) Cabinet partner

The Christian Democrats* Christian Democrats No seats in parliament

The Liberals Liberals (center-right) Opposition

The Conservatives Conservatives Opposition

The Liberal Alliance Liberals (right) Opposition

The Danish People’s Party Nationalists Opposition

*The Christian Democrats are included in this table, but not in the subsequent analyses because a) they were not realistic partners or support parties in any proposed governments due to their low public support (usually no more than 1%), and b) because including them reduces the number of observations as a large number of respondents gave the "do not know" answer when they assigned policy positions to this party.

We replicate the analysis from earlier in Tables 5-7 (substituting the party system in the

United Kingdom with the Danish party system, and substituting the Scottish independence issue

dimension with the refugee issue dimension). The empirical patterns they reveal are remarkable

similar to the patterns we found in the United Kingdom. First, the party of the prime minister is

consistently attributed disproportionate influence across all policy dimensions. For example, the

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Social Democrats are attributed a minimum of 52 percent policy influence as prime ministers on the

economic left-right dimension and the Liberals are attributed a minimum of 39 percent influence on

the same dimension. These numbers are, of course, lower than in the UK because there are more

parties to share the influence, but they still suggest that voters attribute disproportionate influence to

large prime minister parties, which is sensible given what political scientists know about the role of

these parties in the policymaking process – even in power-sharing contexts.

Table 4: Taxation and spending

Party Expected seat

share (Avg.)

PM: LIB Partner: CON Partner: DPP Support: LA

PM: LIB Partner: CON Support: DPP Support: LA

PM: LIB Partner: CON Support: LA

PM: SD Partner: RAD Partner: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: SPP Support: ALT

Unity List (UL) 8 0 0 0 2 4 0 Socialists (SPP) 7 0 0 0 16 12 18 Alternatives (ALT) 4 5 4 1 13 8 8 Soc. Dems. (SD) 27 0 0 0 63 59 52 Radicals (Rad) 8 1 0 3 6 15 19 Liberals (LIB) 24 44 39 53 0 0 0 Conservatives (CON) 5 24 30 19 0 2 3 Liberal Alliance (LA) 6 4 10 23 0 0 0 Nationalists (DPP) 18 22 17 1 0 0 0

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 735.

Second, the results again show that support parties are attributed influence in a way that is

often comparable to that of coalition partners (though with some exceptions like the Liberal

Alliance being attributed 0 percent influence on refugee policy despite being a support party for a

center-right government). For example, the Nationalist party is attributed 22 and 23 percent

influence on refugee policy as a government partner and support party, respectively. In fact, this is

more influence than the conservative coalition partner is ever attributed on this policy dimension.

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Table 5: Refugees

Party Expected seat

share (Avg.)

PM: LIB Partner: CON Partner: DPP Support: LA

PM: LIB Partner: CON Support: DPP Support: LA

PM: LIB Partner: CON Support: LA

PM: SD Partner: RAD Partner: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: SPP Support: ALT

Unity List (UL) 8 0 0 0 5 0 0 Socialists (SPP) 7 0 0 0 17 2 10 Alternatives (ALT) 4 0 0 0 26 38 26 Soc. Dems. (SD) 27 0 0 0 36 34 35 Radicals (Rad) 8 0 0 0 16 26 29 Liberals (LIB) 24 66 61 72 0 0 0 Conservatives (CON) 5 1 16 17 0 0 0 Liberal Alliance (LA) 6 11 0 10 0 0 0 Nationalists (DPP) 18 22 23 1 0 0 0

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 735.

Third, the results are again indicative that issue salience matters. This is most clear for the

DPP, which is attributed more influence than the prime minister as a coalition partner on the highly

salient issue of EU integration (41 versus 35 percent). Interestingly, however, the results also reveal

that the DPP are not attributed nearly as much influence on the issue of refugees despite this also

being a core issue for this party. We think that this is likely because the refugee issue has become

salient to virtually all parties in contemporary Western democracies and the DPP policy position on

this issue has become less differentiated from those of the Conservatives and Liberals. Given that,

voters may have concluded that the DPP would move EU policy towards more national sovereignty

in a center-right government, but that a center-right government would implement stricter

immigration rules regardless of whether the DPP was included in it. This possibility is supported

with the results for the Alternatives, which are attributed a disproportionate level of influence on

immigration policy as a support party in a center-left government, which is a policy area that is not

only salient to the Alternative Party, but also an issue dimension where the Alternatives did occupy

a differentiated position in the center-left government (at least compared to the Social Democratic

prime minister party). Consequently, voters may have sensibly inferred that Social Democratic

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reliance on the Alternative Party in a center-left government would have shifted immigration policy

toward less strict asylum rules.

Table 6: European Union

Party Expected seat

share (Avg.)

PM: LIB Partner: CON Partner: DPP Support: LA

PM: LIB Partner: CON Support: DPP Support: LA

PM: LIB Partner: CON Support: LA

PM: SD Partner: RAD Partner: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: UL

Support: SPP Support: ALT

PM: SD Partner: RAD Support: SPP Support: ALT

Unity List (UL) 8 0 0 0 18 12 15 Socialists (SPP) 7 0 0 0 2 2 6 Alternatives (ALT) 4 0 0 0 10 9 4 Soc. Dems. (SD) 27 0 0 0 67 53 42 Radicals (Rad) 8 0 0 0 0 21 24 Liberals (LIB) 24 35 39 57 3 0 3 Conservatives (CON) 5 16 12 10 0 3 0 Liberal Alliance (LA) 6 8 20 25 0 0 6 Nationalists (DPP) 18 41 29 8 0 0 0

Note: Each column represents a government. Each cell entry represents the percentage policy weight attributed to the party in the row. The number of respondents is 735.

Finally, the results are again indicative that voters use political news and history to attribute

a party’s influence sensibly. From 2001 to 2011 the Danish government consisted of a Liberal PM

party with a Conservative coalition partner, and this government made most of their policy with the

support of the DPP. From 2011 to 2014 election, on the other hand, the government consisted of a

Social Democratic PM party with socialist and radical coalition partners, and with outside support

from the UL. Yet, many key bills were negotiated with the parties right of the ideological center

instead of the UL during this time. In fact, internal dissatisfaction with this pattern appears to have

been a key factor behind the party choosing to withdraw from the government in 2014 and become

a support party instead. until the 2015 election.20 In the decade from 2001 to 2011 the DPP had thus

demonstrated its ability to exert influence on the policymaking process outside of the government

20 The catalyst was internal dissatisfaction within the SPP after the government sold a large portion of an energy company to a subsidiary of Goldman Sachs.

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whereas the SPP and the UL had not publically demonstrated this ability. Accordingly, we see that

the DPP is never attributed less than 17 percent policy influence as a support party on any given

policy dimension whereas the SPP and the UL are never attributed more than 12 percent. The

results presented here and earlier thus collectively suggest that voters not only use heuristics to infer

policy responsibility in sensible ways, but also political news and history.

Conclusion

Democratic theorists have long argued that voters are unable to hold their representatives

accountable when there is a “plurality in the executive”. Using unique survey data from 5

parliamentary countries with coalition government we have illustrated that the argument is flawed.

Specifically, we have shown that voters use party characteristics such as party roles and party sizes

to infer responsibility in coalition government contexts, and these are characteristics that other

research suggest are related to actual policymaking. Furthermore, we have shown that voters use

issue salience to infer a party’s influence on a particular issue dimension, and that they even take

the collaborative history of parties into consideration when they develop their influence inferences.

Of course, much remains to be done. One important extension of the work presented here is

a test of how our responsibility attribution measure interacts with perceptions of the economy. Our

results suggest that when voters perceive that the economy is doing poorly then the main electoral

beneficiaries should be small parties (e.g. niche parties), and the main electoral losers should be

prime minister parties (or, at least, perceived prime minister parties). Testing this possibility is

beyond the scope of this paper, but it comports with anecdotal evidence (e.g. the electoral

experience in Greece following its economic crisis), and we will test it in future work.

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