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

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1 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

2 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.

3 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.

4 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.

5 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.

6 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).

7 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.

8 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

9 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

10 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

11 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).

12 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

13 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

14 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.

15 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.

16 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 policymaking 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.

17 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 11 The 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.

18 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).

19 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

20 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

21 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

22 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 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.

23 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 *** *** *** ** *** (0.00) (0.00) (0.00) (0.00) (0.00) Median party (0.05) (0.05) (0.05) (0.04) (0.06) Centrality ** (0.01) (0.01) (0.02) (0.01) (0.02) Party ** 1.457*** *** * 1.507*** (0.06) (0.08) (0.11) (0.09) (0.14) Party *** *** *** (0.08) (0.07) (0.13) (0.10) (0.07) Party *** *** *** *** 0.429*** (0.09) (0.07) (0.08) (0.10) (0.09) Party *** 0.537*** *** *** 0.845*** (0.08) (0.07) (0.09) (0.10) (0.10) Party *** 0.699*** *** *** *** (0.12) (0.07) (0.10) (0.09) (0.08) Party *** 0.766*** *** *** - (0.08) (0.07) (0.11) (0.11) Party *** 1.404*** ** - (0.14) (0.12) (0.09) Party *** *** - (0.07) (0.07) (0.10) Party *** - (0.07) (0.11) Cut point *** 0.145* *** *** *** (0.13) (0.07) (0.11) (0.13) (0.10) Cut point *** 1.311*** *** (0.13) (0.07) (0.11) (0.13) (0.10) Cut point *** 2.359*** 1.554*** 1.062*** 2.102*** (0.13) (0.07) (0.11) (0.13) (0.11) Cut point *** 3.539*** 2.918*** 2.291*** 3.231*** (0.13) (0.08) (0.11) (0.13) (0.12) Random intercept 0.282*** 0.519*** 0.476*** 0.411*** 0.649*** variance: 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

24 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

25 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.

26 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:

27 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 X G = i G α i x i, 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 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.