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date: 13 December 2018

Electoral Systems and Issue Polarization

Abstract and Keywords

This chapter reviews theoretical and empirical research pertaining to the question: How do electoral systems influence parties’ programmatic incentives, that is, the policy positions party elites present to the public? More specifically, it discusses whether electoral systems influence the diversity of party policy positions, measured via the degree of party system polarization. It emphasizes electoral laws’ permissiveness or proportionality, defined in terms of the relationship between parties’ national vote shares and their share of parliamentary seats. The review of theoretical arguments suggests that any effects of proportionality on polarization should be modest, a prediction supported by empirical studies that identify only weak and inconsistent relationships between proportionality and party polarization along the left–right ideological dimension.

Keywords: parties, polarization, policies, electoral systems, representation

This chapter reviews theoretical and empirical research pertaining to the question: How do electoral systems influence parties’ programmatic incentives, that is, the policy positions party elites present to the public? More specifically, we discuss whether electoral systems influence the diversity of party policy positions, measured via the degree of party system polarization. We emphasize electoral laws’ permissiveness or proportionality, defined in terms of the relationship between parties’ national vote shares and their share of parliamentary seats.

The link between electoral systems and party system polarization matters because it pertains to the range of choices the party system provides to the electorate. When competing parties differentiate their issue positions from each other, voters confront diverse policy options, which enhance their abilities to direct government policy outputs via their votes (e.g., Powell 2000; McDonald and Budge 2005). Party system policy diversity has been linked to other features of mass-elite linkages including citizens’ satisfaction with democracy (Ezrow and Xezonakis 2011), voters’ abilities to hold governments accountable for national economic conditions (Hellwig 2012), and the degree to which voters punish parties for scandals and incompetence (Clark and Leiter 2014).

As we discuss later, empirical research on how electoral systems affect party system polarization has only emerged over the past fifteen years, primarily due to earlier limitations on cross-nationally comparable measures of parties’ policy positions. Moreover, empirical studies on this topic typically analyze party system polarization in terms of a unidimensional left–right continuum associated with long-standing policy debates over social welfare programs, taxes, and government intervention in the economy. At the same time, theoretical arguments about how electoral systems affect party system (p. 248) polarization are more developed. Next we review these previous arguments (and propose some new arguments of our own), along with the empirical evidence reported in earlier studies. We conclude by discussing the implications of these findings and directions for future research.

Party System Polarization and Electoral Systems: Theoretical Arguments

Theoretical and empirical studies analyze the factors that influence parties’ programmatic incentives, including parties’ policy responses to public opinion as a whole (e.g., Ward, Ezrow, and Dorussen 2011; Adams, Clark, Ezrow, and Glasgow 2004; Ezrow 2008); opinion among electoral subconstituencies including parties’ core supporters, the politically sophisticated, and the affluent (Ezrow, De Vries, Steenbergen, and Edwards 2011; Schofield and Sened 2006; Gilens and Page 2014; Adams and Ezrow 2009); past election results (Budge 1994; Laver 2005; Somer-Topcu 2009); rival parties’ policy positions (Han 2015; Spoon 2011; Williams 2015); parties’ public images for competence and integrity (Adams and Merrill 2009; Clark 2014); parties’ organizational characteristics (Schumacher, De Vries, and Vis 2013); and global economic conditions (e.g., Haupt 2009; Weschle forthcoming).1 Later we review empirical studies on whether electoral systems influence party positions and, through these positions, party system polarization. First, however, we review the theoretical arguments pertaining to this issue. We consider the questions: Should we expect that electoral systems condition parties’ strategic incentives to announce more radical or moderate policies, and to differentiate their policy positions from each other? And assuming the answer to this question is yes, should we expect these effects to be substantively significant, that is, that electoral system proportionality exerts a major influence on polarization? The first question is interesting because theoretical arguments point in conflicting directions. However, we believe the second question has a straightforward answer, namely, that we have strong theoretical reasons to expect electoral systems to exert at most modest effects on party system polarization.

Why Electoral Proportionality Should Exert Only Modest Effects on Party Polarization

The fist reason to doubt that electoral systems strongly affect party system polarization is that polarization at times varies sharply over time within countries that do not change their electoral systems—which conflicts with the hypothesis that voting systems are the (p. 249) primary drivers of party system polarization. This pattern is seen in the United States and Britain, which have continuously employed the highly disproportional plurality (first-past-the-post) system, but where party system polarization has fluctuated sharply over time. In Britain, the post–World War II period initially featured highly consensual policy competition between the dominant Labour and Conservative Parties, which both endorsed the “postwar settlement” policies of higher taxes, extensive social welfare benefits, and Keynesian demand management (Garnett and Lynch 2016). Yet this postwar policy convergence was succeeded by dramatic party system polarization, with the Conservatives shifting sharply to the right under Margaret Thatcher beginning in the mid-1970s, while Labour shifted leftward in the early 1980s under the leadership of Michael Foot. This 1980s period of elite polarization was followed by a second period of party system convergence beginning when Tony Blair shifted “New Labour” toward the center ground starting in the mid-1990s, a moderation strategy the Conservatives subsequently pursued from 2006 onward under David Cameron (see Adams, Ezrow, and Somer-Topcu 2011).2 The US party system displayed a dynamic similar to Britain’s until the mid-1990s, in that the Democratic and Republican Parties converged programmatically on many issues from the end of World War II through the 1970s, prompting the American Political Science Association to publish a famous paper decrying the lack of meaningful policy alternatives on offer to American voters (American Political Science Association, Committee on Political Parties 1950). However, the parties have dramatically polarized over the past thirty-five years, with Republican elites shifting sharply rightward under the leadership of President Ronald Reagan and his successors, while the Democratic Party has shifted programmatically to the left (Carroll, Lewis, Lo, McCarty, Poole, and Rosenthal 2011). Finally, proportional representation (PR)-based systems at times exhibit similarly sharp over-time fluctuations in party system polarization. In the PR-based Dutch system, for instance, the two largest parties, the Christian Democratic Appeal (CDA) and the Labour Party (PvDA) were sharply polarized up to the mid-1980s, but then converged substantially across the next decade (Adams 2012; Ezrow and Xezonakis 2011), while in the PR-based German system the sharp left–right policy divide between the Social Democrats and the Christian Democrats narrowed substantially between 2005 and 2009 and again since 2013, when these parties cooperated in a national coalition government. If proportionality is the primary driver of polarization, how do we explain dramatic party polarization changes over time within countries that do not change their electoral laws?

The second reason to doubt that proportionality substantially affects party polarization is to note the long list of additional factors that have been shown to influence party policy positions. As discussed earlier, previous studies document that party positions respond to public opinion, past election results, parties’ organizational characteristics, their images with respect to competence and integrity, and economic conditions. Intuitively, if electoral laws are at most one of many factors influencing party policy strategies, one might doubt that electoral laws by themselves substantially affect polarization. (p. 250)

We believe the considerations outlined earlier, that many factors besides electoral systems influence party policy positions, and that party system polarization at times fluctuates sharply within countries that have not changed their electoral systems, suggest that these systems do not strongly influence the degree of elite polarization.

To the Extent Proportionality Matters, Should It Promote Party System Polarization or Convergence?

We next consider the question: To the extent that electoral systems influence system polarization, should we expect more proportional laws to enhance or depress polarization? This question is interesting because theoretical arguments point in conflicting directions. The argument that proportionality increases polarization is, first, that parties in plurality-based electoral systems (including the French majority-plurality system, described in Hoyo’s chapter in this volume) plausibly experience greater pressure to maximize votes, since winning seats requires that a party’s candidate finishes first in a district, whereas more proportional, multiseat district systems provide easier parliamentary access to smaller parties. And given survey-based evidence that the distribution of voter ideologies in most democratic publics is heavily concentrated near the center of the left–right scale (see, e.g., Powell 2000; Adams and Somer-Topcu 2009), there is an intuitive logic that parties maximize votes by offering moderate policies, all else equal. This logic might motivate the parties contesting plurality-based elections to present more moderate, vote-maximizing policies than do the parties contesting PR-based elections (Dow 2001).3

As a second, related, point, the fact that some voters strategically desert smaller parties’ candidates under disproportional voting systems to avoid “wasting” their votes on smaller parties with no realistic chance of winning seats in the district (Cox 1997; Moser and Scheiner 2004) further enhances plurality-based parties’ strategic incentives to promote moderate policy agendas that make them electorally competitive. Third, Kedar (2009) documents that voters in proportional electoral systems with multiparty coalition governments are more willing to vote for radical parties, recognizing that such parties cannot fully implement their radical policy promises in a governing coalition but may at least pull government policy outputs away from their moderate coalition partners, in the voter’s preferred direction (see also Grofman 1985; Adams, Merrill, and Grofman 2005). To the extent that radical parties are more attractive to voters in proportional systems that feature more power sharing, the parties competing in PR systems have greater electoral leeway to promise radical policies. Finally, given that proportional electoral systems tend to increase the number of competitive political parties (see the chapter by Shugart and Taagepera in this volume), in particular that plurality-based systems are associated with two dominant parties, the Downsian logic of two-party convergence (Downs 1957) should apply more strongly to the smaller party systems in countries with disproportional voting systems.4 (p. 251)

At the same time, alternative considerations suggest that electoral permissiveness may not increase party system polarization. First, to the extent that parties seek membership in the multiparty cabinets that typically govern under proportional representation, parties have strategic incentives to present nonradical policies that make them attractive coalition partners to the large, moderate, mainstream parties of the center-left and the center-right that are typically tasked with forming a government (Martin and Stevenson 2001). Thus, even if seat-seeking parties in PR-based systems can win parliamentary representation while espousing radical policies, cabinet-seeking parties (i.e., parties that aspire to join the government) may feel pressure to present more moderate positions. In this regard, Ezrow (2008) notes that centrist party positioning provides a greater number of potential coalition partners, so that moderate positions may prove attractive to small, cabinet-seeking parties in proportional systems.

Second, while the central argument that plurality-based systems prompt party policy convergence is that plurality systems enhance parties’ incentives to present moderate, vote-maximizing positions, there are theoretical and empirical reasons to question whether moderate positioning actually enhances party support. Theoretically, spatial modeling studies advance reasons parties may maximize votes by presenting noncentrist—even radical—policies, including the consideration that such policies will prompt party activists, who trend to be ideologues, to contribute scarce campaign resources to the party (e.g., Schofield and Sened 2006; Moon 2005); the desire to maximize turnout among more radical party supporters who may abstain if they perceive the party abandoning its core principles (Adams et al. 2005, chap. 7–9); and the need to deter radical protest parties from entering the system and “outflanking” an established, moderate party (Calvert 1985). Empirically, cross-national studies reach conflicting conclusions about whether moderate policy positioning meaningfully enhances party support: Ezrow (2007) reports analyses that support this proposition; Adams and Somer-Topcu (2009) find little evidence that policy moderation systematically affects party support; and remarkable research by Karreth, Polk, and Allen (2013) documents that Social Democratic parties that pursued a “Third Way” policy moderation strategy increased their support in the short run but suffered longer-term reverses as their core supporters subsequently deserted the party. In this regard, the highly visible electoral successes enjoyed by sharply noncentrist elites such as the British Conservatives under Margaret Thatcher and the Republican candidate Ronald Reagan (and his Republican successors) also cast doubt on the maxim that the key to electoral success in plurality-based systems is to “occupy the center ground.”

Finally, we note that extensive empirical research documents many non-policy-related considerations that influence voters’ decisions including economic conditions (e.g., Powell and Whitten 1993), parties’ images for competence and integrity (Clark 2009, and voters’ long-term party identifications growing out of their early socialization experiences (e.g., Campbell 1960; Campbell, Converse, Miller, and Stokes 1960). And the “issue ownership” perspective on elections posits that voters are more easily moved by the issue areas that competing political parties emphasize than by the specific positions they stake out within these areas (e.g., Petrocik 1996; Green and Jennings (p. 252) 2012). This research casts doubt on whether parties’ issue positions will substantially affect their support.5

In toto, the considerations outlined previously do not provide strong guidance about whether electoral system proportionality tends to increase party system polarization. Disproportional, plurality-based electoral systems may prompt parties to prioritize maximizing their electoral support, which may push parties toward the center of the voter distribution—provided elites believe that policy moderation is a vote-winning strategy. Yet we have outlined the reasons to doubt that “occupying the center ground” actually attracts many additional votes. Moreover, we have noted that even if seat-seeking parties feel more leeway to stake out radical positions in proportional electoral systems, parties seeking to enter the cabinet likely experience pressure to moderate to be an acceptable coalition partner. Hence, theoretical arguments about how electoral system proportionality affects party system polarization point in conflicting directions. However, we do see strong reasons to expect the net effect of proportionality on polarization—whether positive, negative, or neutral—to be modest.

Party System Polarization and Electoral Systems: Empirical Results

An Empirical Focus on Parties’ Left–Right Positions

With important exceptions discussed later, empirical studies of electoral systems and party polarization analyze party positions strictly in terms of the unidimensional left–right continuum, a focus motived by both theoretical and practical considerations. Theoretically, the left–right dimension—typically associated with long-standing debates over taxes, social welfare policy, and government intervention in the economy—is arguably the only dimension that travels across all Western democracies, thereby permitting meaningful cross-national comparisons of party positions. The related, more practical consideration is that until the recent releases of the codings of party manifestos provided by the Comparative Manifesto Project and of experts’ cross-national party placements by the Chapel Hill Expert Survey team, there were no available cross-national measures of party positions along more specific dimensions that could be used to construct issue-specific measures of party system polarization.

Measuring Party System Polarization and Electoral Law Proportionality

Empirical studies on whether proportionality affects elite polarization must first define and measure these concepts. With respect to polarization, some studies measure parties’ (p. 253) left–right positions based on codings of parties’ election manifestos (e.g., Budge and McDonald 2006; Matakos, Troumpounis, and Xefteris 2016), others analyze voter perceptions of party positions (Dow 2011), others employ factor analyses of voter election surveys (Dow 2001), and still others study political experts’ party placements (Ezrow 2008). Moreover, studies differ on how to measure overall polarization, with some studies emphasizing a measurement analogous to the standard deviation of the party positions in the system (e.g., Ezrow 2008; Dow 2011)6 and others emphasizing the distance between the two most extreme parties in the system (e.g., Budge and McDonald 2006; Andrews and Money 2009). However, as discussed later, empirical studies’ conclusions on how electoral systems affect party polarization do not typically turn on these measurement issues, because alternative measures of party left–right positions (manifesto codings, expert surveys, voters’ party placements, etc.) all correlate strongly with each other (Dalton and McAllister 2015), as do alternative measures of party system polarization (Best and Dow 2015).

Electoral system proportionality can be computed independently of specific election results, based on the average number of seats available per district (district magnitude),7 while alternative, election-dependent measures use election results to measure proportionality, including Gallagher’s (1991) disproportionality index, which aggregates the discrepancies between parties’ national vote shares and their seat shares. A consistent finding from this literature is that systems of single-seat districts, such as those used in Britain, Canada, and France, are disproportional compared to PR systems with larger district magnitude, because smaller parties’ candidates rarely finish first in a district, so that small parties’ parliamentary seat shares under these systems typically fall well below their national vote shares (Shugart and Taagepera 2017).8 Several of the empirical studies on electoral systems and party system polarization discussed later employ both proportionality measures and typically find that both measures support similar conclusions. The fact that substantive conclusions do not turn on issues pertaining to the measurement of party polarization and proportionality simplifies our task, and in our empirical literature review we will not discuss how different studies measure these concepts, except in the rare cases where this issue affects the authors’ substantive conclusions.

Overview of the Literature: No Consistent Findings on Whether Proportionality Affects Party Polarization

Empirical studies reach conflicting conclusions on whether proportionality increases party polarization. In the first cross-national study on this issue, Dow (2001) analyzes national election surveys from four countries, two with disproportional electoral systems (France and Canada) and two with highly proportional systems (Israel and the Netherlands), concluding that the major political parties were more polarized in the proportional systems.9 In a follow-up study, Dow (2011) extends this research to thirty (p. 254) democracies between the mid-1990s and the mid-2000s and reaffirms the positive association between proportionality and left–right party polarization. Matakos et al. (2016) build on Dow’s research by analyzing nearly fifty years of party manifestos from over twenty industrialized countries and substantiate Dow’s conclusion.

At the same time, alternative empirical studies cast doubt on whether proportionality meaningfully increases party polarization. Dalton (2008), analyzing a dataset similar to that of Dow (2011), reports a detectable but substantively weak relationship between left–right proportionality and polarization, while Ezrow (2008) finds no relationship between these variables in analyses of party positions from fifteen party systems during the 1980s. Similarly, Andrews and Money (2009) find no relationship between proportionality and party polarization, on either social or economic policy dimensions, while Curini and Hino (2012) extend the voter surveys used in Dow (2011) to analyze thirty-three party systems and find no evidence that electoral proportionality directly increases left–right polarization.

Finally, scholars have analyzed whether proportionality influences party system polarization indirectly via the electoral system’s effect on the number of competitive parties, based on the logic that the larger number of parties associated with proportional systems (see the Shugart and Taagepera chapter in this volume) may become more “crowded” near the center, pushing vote-seeking parties toward more radical policies (see Downs 1957; Cox 1990). Here too the literature reaches conflicting conclusions, with Dalton (2008), Ezrow (2008), and Dow (2011) finding no evidence that the number of competitive parties influences the degree of left–right party polarization, while Andrews and Money (2009) and Matakos et al. (2016) find some (inconsistent) evidence of a positive relationship between these variables.10

What Substantive Conclusions Can We Draw from the Literature?

In toto, the literature on how electoral system proportionality influences party system polarization reaches inconsistent conclusions, in that Ezrow (2008) and Andrews and Money (2009) detect no relationship between these variables; Dalton (2008) and Curini and Hino (2012) estimate weak and inconsistent relationships; and Dow (2001, 2011) and Matakos et al. (2015) estimate that polarization systematically increases with proportionality. Moreover, these studies’ conflicting conclusions do not stem from different approaches to measuring party positions or to defining either party polarization or proportionality.

At the same time, we believe that empirical studies, in combination with the arguments outlined earlier, support some tentative conclusions. First, both theory and empirics provide reasons to reject the hypothesis that proportionality actually depresses polarization; that is, parties do not systematically take morepolarizedpolicy positions in more proportional electoral systems. As discussed earlier, the results reported in (p. 255) empirical studies range from findings of no detectible relationship between proportionality and polarization to findings that party polarization systematically increases with proportionality. And the theoretical arguments suggest that any such effect will likely be modest, given the wide range of additional factors that influence party policy strategies (public opinion, past election results, economic conditions, etc.). This perspective is substantiated by the studies of Ezrow (2008) and Andrews and Money (2009) that report no detectible effects of proportionality on party polarization, and also by Dalton (2008) and Curini and Hino (2012), who report weak and inconsistent relationships. Moreover, even the two empirical studies that find that proportionality detectibly enhances left–right polarization estimate relatively modest effects. Matakos et al. (2016) estimate that a shift from the most majoritarian to the most proportional electoral systems in their sample increases the predicted distance between the two most extreme party platforms in the system by about 1.5 points on a 10-point scale. While the weighted party policy extremism measure discussed by Dow (2011) is harder to interpret, the magnitudes of the effects Dow estimates appear smaller than those estimated by Matakos et al. (2015).11 We believe these estimates support the conclusions that (1) electoral proportionality exerts at most modest effects on party system polarization and (2) the effect of greater proportionality—if any effect exists—is to increase polarization.

Finally, we re-emphasize two constraints on studies of proportionality and party polarization. First, in cross-national comparisons linking proportionality to polarization, the number of cases is limited to the number of different democratic party systems in the world. Hence, unlike studies of political behavior that analyze survey responses from thousands of citizens, our unit of analysis is the party system and the country’s electoral system; moreover, since democracies rarely enact substantial electoral system changes, empirical studies on this topic typically have fewer than thirty-five observations (and several studies have fewer than twenty observations).12 These small samples hamper analysts’ abilities to parse out how electoral system proportionality affects party system polarization. Given that the recent studies of Dow (2011), Curini and Hino (2012), and Matakos et al. (2015) already include most of the world’s Western democracies, there is little more scholars can do to solve this small-N problem.

Conclusion and Discussion

The extant theoretical and empirical literatures do not clearly answer the question: Does electoral system proportionality increase party system polarization? Some theoretical arguments suggest the answer is yes, yet other arguments cast doubt on this proposition; some empirical studies conclude that proportionality detectably increases polarization, yet other studies report no detectable effects. This uncertainty notwithstanding, we see no theoretical or empirical reason to believe that proportionality actually depresses party polarization, that is, that greater proportionality promotes party policy convergence. The questions remain: Does proportionality actually increase polarization, and if (p. 256) so, how large are these effects? Our review of the relevant scholarship suggests that the answer to the first question is “maybe,” while the answer to the second question is “any such effects are probably modest.”

We close with some suggested directions for future research. First, given that most empirical studies on electoral laws and party policy positioning analyze the unidimensional left–right policy continuum, future studies might profitably develop multidimensional measures of party polarization. This approach seems feasible based on analyses of both parties’ election manifestos and the issue-specific party position measures available through the widely used Chapel Hill Expert Survey (CHES) datasets. Indeed, Rexford’s (2017) recent analyses of the CHES data uncover evidence that electoral permissiveness13 modestly increases party system polarization with respect to more-specific issue dimensions. Rexford also demonstrates that electoral permissiveness enhances large parties’ tendencies to “hedge their bets” by taking inconsistent stands across different policy dimensions.

Second, and related, it seems possible that electoral systems influence parties’ incentives to develop distinctive issue emphases with respect to cross-cutting policy dimensions. In this regard, more proportional electoral systems may facilitate the emergence of “niche” parties such as green, radical right, agrarian, and ethno-territorial parties that emphasize specific policy dimensions (the environment, immigration, agriculture, and so on) that do not map onto long-term left–right economic policy debates. Rexford’s (2017) research provides preliminary support for this hypothesis: he demonstrates that while smaller “limited issue” parties will be inclined to heavily emphasize their core issues (e.g., the Greens with the environment, nationalist parties with immigration, and so on) regardless of the electoral context, greater electoral permissiveness motivates larger parties to confront smaller parties on their core issues, so that large parties place more emphasis on smaller parties’ core issues as electoral permissiveness increases.

Finally, an emerging strand of research analyzes the causes and consequences of party policy ambiguity, that is, the factors that motivate parties to present clear as opposed to ambiguous policy messages to the electorate (e.g., Kernell 2016; Somer-Topcu 2015). Here too, we might expect the nature of the electoral system to influence parties’ strategic calculations about the clarity of their policies.

In this chapter we have analyzed the connection between electoral rules and the dispersion of rival parties’ policy positions. The scholarship reviewed in this chapter does not conclusively establish the nature of this relationship, but it provides a positive basis for future research.


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(1.) Additional research documents the conditional nature of these relationships, for instance, that the “openness” of the domestic economy mediates parties’ responses to public opinion (Ward et al. 2011; Ezrow and Hellwig 2014), as do parties’ organizational characteristics (Schumacher et al. 2013), along with party type, that is, niche versus mainstream parties (Adams, Clark, Ezrow, and Glasgow 2006). See Adams (2012) for an overview of this literature.

(2.) We note that the post-2010 period in British politics has arguably seen the beginnings of renewed Labour–Conservative polarization, as the Conservatives in government (in coalition with their junior partner the Liberal Democrats between 2010 and 2015) have enacted more right-wing economic and social policies than was implied by the moderate policy rhetoric their leader David Cameron issued during the 2006–2010 period of opposition, while the Labour Party electorate selected the sharply left-wing leader Jeremy Corbyn in the 2015 leadership contest.

(3.) Dow (2001) also notes that given the well-known fact that plurality-based systems often “manufacture” a parliamentary majority for the largest party—that is, the largest party wins a majority in parliament with a national vote share below 50 percent—parties contesting plurality-based elections are more likely to believe that the only viable pathway to being in government and enacting desired policy change is to maximize their electoral support.

(4.) Eaton and Lipsey (1975), Cox (1990), and Merrill and Adams (2001) present spatial models of elections that predict that, all else equal, larger party systems motivate vote- and seat-seeking parties to promise more radical policies. McGann (2002) extends this spatial modeling logic to systems where parties are responsive to their activists.

(5.) This intuition is consistent with simulations on election survey data reported by Erikson and Romero (1990), Schofield and Sened (2006), and Adams et al. (2005), all of which conclude that parties’ expected votes do not vary significantly with their policy images so long as the parties do not propose truly extreme positions.

(6.) Additional variations include whether to weight each party’s position by its vote/seat share, and whether to standardize the dispersion of parties’ ideologies against the dispersion of voter ideologies (see Ezrow 2008; Alvarez and Nagler 2004).

(7.) Typically, the logarithm of this measure is used to deal with the right-skewed distribution arising from single nationwide districts used by some countries (e.g. Slovakia, Israel).

(8.) The American plurality system is an exception to this generalization, because few votes are wasted on third-party candidates and thus most elected representatives win 50 percent of the vote, unlike in the other systems discussed here.

(9.) Dow’s (2001) study, which reports factor analyses of citizens’ survey responses, does not precisely specify which positional dimensions the parties contest, although Dow notes the strong reasons to believe that one of the dimensions denotes left–right issues in all of the countries.

(10.) Curini and Hino (2012) estimate that larger party systems are associated with more party polarization only when there is no expectation of a coalition government.

(11.) Dow’s estimates imply that a shift across the entire range of proportionality values for the thirty democracies in his dataset will increase the average party’s predicted left–right distance from the median party by roughly 0.5 units, along the zero-to-ten scale.

(12.) We note that some recent studies, notably Makatos et al. (2015), analyze multiple observations of party polarization within each country by including election-specific measures based on analyses of parties’ election manifestos, which increase the number of observations. However, since these analyses necessarily cluster the data by country, incorporating multiple observations per country generates more reliable measures of the average degree of party polarization in each country, but without solving the small-N problem.

(13.) Rexford proxies “permissiveness” via the seat product (which is explained in the chapter in this volume by Shugart and Taagepera).