Are Americans polarized on issue dimensions?

ABSTRACT American mass polarization is still a contested subject in political science. One reason why scholars disagree is because polarization has often been studied either using individual issue questions or using an overall measure of ideology (usually ideological constraint). Because these methods are problematic, I use a multidimensional approach to estimating ideology. Since scholars have disagreed on what issue domains are important for Americans, I use exploratory factor analysis to show that there are three major ones: economics, race, and morality. I then use a latent measurement model to construct ideal points on all three beginning in the year 1988 going through to 2016. Then I evaluate polarization both as an increase in dispersion and as a state of how bimodal the distribution is. Although I find increased dispersion on all the dimensions since 1988, the key finding of this study is that the level of polarization is dependent on the dimension–Americans are more polarized on race and morality in 2016 than they are on economics. Still, all the distributions are centrally distributed even in 2016. Hence, polarization could still become a lot worse than it was in 2016.

(2016, 1) states that "America is polarized. Our political parties are highly polarized and the American electorate is highly polarized." The scholarship has of course progressed since this point, but no new innovations have emerged since the Fiorina-Abramowitz debate-at least none that the literature has coalesced around as the answer. Most of them simply try to reinforce the findings of these two authors. The inability of scholars to come to a consensus on this research question is troubling, especially when one realizes that the top two scholars in this area-Fiorina and Abramowitz-are both analyzing the same data. How can these two strikingly different empirical findings be reconciled? This is the task that I tackle in this paper. I will focus on the Fiorina-Abramowitz debate since they are the most vocal and most cited authors in this literature. Although both of them analyze many aspects of polarization, I focus on their disagreement over societal polarization on issues-as presented in   Figure 17-3a and Abramowitz (2010) Figure 3.1-to keep the analysis manageable. Thus, I will not even touch affective polarization (an area in which the literature has now become very focused on) because this is not the way polarization has traditionally been understood in the literature, at least not in the Fiorina-Abramowitz debate. 2 I will also not address ideological sorting as that is a different concept from polarization. Lest there be any confusion, I want to make it clear that I do not make any major theoretical contribution in this paper. I am simply synthesizing arguments and methods made by others in a way that has not been done before.
I claim that the inability of the polarization literature to come to a consensus is because of two main reasons. First, they have vastly different ways of translating survey questions into measures of ideology. On one hand, Abramowitz measures each person's ideological consistency. On the other hand, Fiorina simply analyzes a particular set of issues individually. Second, as Niemi, Weisberg, and Kimball (2011, 235) suggest, they cannot seem to agree on what the standard for polarization should be. Fiorina's standard seems to be people's ideal points clustering at the extreme ends of the distribution. Abramowitz seems to take any divergence over time in the distribution as evidence of polarization.
In this paper, I do six things. First, I give reasons why the methods of Abramowitz and Fiorina in estimating ideology both fall short of what is necessary to study polarization. Ideological constraint is not a good way to estimate ideology when analyzing polarization-as the term has traditionally been understood-because it does not allow for extremism. Using individual issue questions-although it is a better measure than constraint-is also not ideal due to the presence of measurement error. Instead, I argue that it is best to use the advances in political psychology to estimate people's latent opinions in issue areas. Second, using data from the American National Election Study (ANES), I show that the major issue dimensions in America are the government's role in economic affairs (sometimes referred to as social welfare), racial attitudes towards African Americans (henceforth race), and morality. Third, I estimate respondents' ideal points on these issue dimensions using confirmatory factor analysis (CFA). Fourth, I do a theoretical analysis of the different types of measurements of polarization found in the literature. These methods can be applied to the two types of polarization-a state of the world (bimodality) and increasing dispersion over time. I find that one should not rely on a cutpoint for the bimodality measure to determine if a distribution is polarized or not. Rather, this measure is best used to detect changes in the distribution over time. Fifth, I then evaluate the distributions of these three issues using these two different concepts of polarization. Finally, I evaluate how many consistent extremists (people who have extreme views in all three policy areas) exist in the American population.
My conclusion about polarization is more nuanced than either Fiorina or Abramowitz admit in their research. Americans have become more dispersed on all three dimensions, but the distributions on each remain centrally distributed and not bimodal. A critical finding is that the level of polarization depends on the issue domain: Americans are much more dispersed on race and morality than on economics. Furthermore, there is little evidence of many consistent extremists in the American public. Thus, while the assertion that Americans are no more divided than they were half a century ago is false, the assertion that we live in a deeply divided society is also false.

Theoretical discussion
One of the major problems the literature has is conflating societal polarization with party polarization. In this paper, I choose to concentrate on societal polarization-in the spirit of DiMaggio, Evans, and Bryson (1996). Thus, I do not analyze the differences in society in any subgrouping (especially partisans). My avoidance of party polarization makes any question of sorting, which is a large point of debate in this literature, irrelevant. Furthermore, my research question does not ask why people are polarized. Such a topic is interesting, but again, to keep the analysis manageable, this question is better for another research project. My task here is simply to identify the relevant dimensions of ideology, place people on those dimensions using survey questions, and then decide whether or not people (as a whole) are polarized on those dimensions.
Out of all the ways in which people can be polarized, I choose to focus on ideological polarization because it is the traditional way that the political science literature has understood polarization. Yet, even with this focus, there are still many possible routes to study this. Campbell (2016) and Kinder and Kalmoe (2017) focus on ideological self-placement polarization. 3 This is an important research area indeed, but I choose not to focus on it in this particular paper because, as Ellis and Stimson (2012, 16) note, ideological self-placement is highly subjective to one's own viewpoint-a person who considers himself to be very liberal while living in rural Alabama might be considered a moderate person in San Francisco. Hence, I focus on polarization of issues.
The disagreement over ideological polarization in the Fiorina-Abramowitz literature can be summarized in Figure 1 from Abramowitz and Figure 2 from Fiorina. Both of these graphs are following the societal polarization analysis of DiMaggio, Evans, and Bryson (1996). Furthermore, both use the 2004 ANES with almost the exact same questions (Abramowitz adds the abortion question). Yet, the authors come to very different conclusions based on their distinct analysis. When one looks more closely at these two different figures, one can dissect why these authors disagree. First, there is a lack of agreement over how to take issue questions in surveys and translate them into ideal points. Second, there is a lack of agreement over any definition of polarization. Fiorina views central tendency as proof that there is no polarization. Thus, Fiorina might conclude that Figure 1 shows that there is no polarization in the mass public. On the other hand, Abramowitz sees increasing dispersion over time in the distribution as proof that there is polarization. The following is a discussion behind the theory and methods that Fiorina and Abramowitz are assuming in their research and what the solutions are to the conflict between them.

The measurement of ideal points
As many political scientists know, ideology is a complex concept. In trying to operationalize it, Fiorina and Abramowitz have gone to two extremes: they either assume that people have one ideal point or that they have an ideal point on each single issue. In the first case, the researchers want to study ideology as whole, measuring how consistently liberal or conservative people's opinions are. They do this by putting people into the tertiary category of liberal, moderate, and conservative camps on each issue question and then aggregate all of the questions together to get a measure of ideological consistency (Abramowitz 2010;Abramowitz and Saunders 2008;Lelkes 2016;Pew Research Center 2014). Abramowitz (2010, 118) constructs a libcon11 measure in this way, which I show a similar graph in Figure 1 for the years 1984 and 2004.
There is a major problem with operationalizing ideology in this way: it assumes that ideology is unidimensional. But there is good reason to believe that ideology is multidimensional Snyder 2006, 2008;Conover and Feldman 1981;Feldman 2013;Goren 2012;Klar 2014;Treier and Hillygus 2009) with issues being grouped into areas since, for example, taxation policy has nothing to do with abortion policy. When one assumes multidimensional preferences, a measure of ideological constraint is problematic for the study of polarization. To see why, consider Figure 3 where the issue dimensions are morality and economics. 4 It is easy  Abramowitz (2010). There are slight differences from his, but I replicated it as best as I could to place Tim and Kate as consistent extremists (people who are both ideologically consistent and extreme in their political opinions). It is also easy to see that Ted and Fred are moderates who are also ideologically consistent-Ted's ideal point falls on the liberal side on both issues and Fred's is on the conservative side (as opposed to Bea who is liberal on morality but conservative on economics). The problem is that an ideological consistency measure is putting the Ted-Fred and the Tim-Kate scenarios into the same bucket by just measuring that Tim and Ted are both liberals and Fred and Kate are both conservatives. But these studies do not say anything about the extremity of people's preferences. Hence, a measure of ideological consistency will not capture the fact that Tim and Kate are highly dispersed while Fred and Ted are not. I avoid this problem altogether by (1) using questions which allow people to respond in extreme ways (five or seven point scales) instead of using questions which have options such as agree/neutral/disagree and (2) by not using a measure of constraint as a measure of ideology.
In the second case, other political scientists have gone to the opposite end and presupposed that Americans have an ideal point on every issue. Although Fiorina never states this explicitly in his writings, it is the obvious premise when one deconstructs that Americans have values on broad issues but often have trouble expressing those values when asked about individual issues on a survey. As Achen (1975) argued, these individual questions have a lot of measurement error in them. This could be a reason why there is moderation on all of the questions which Fiorina analyzes. There are more advanced ways of estimating ideal points. In political psychology, there has been much progress in determining people's latent opinions. Layman and Carsey (2002) and Goren (2012) both use CFA to determine people's ideal points. Since this methodology is used by such notable researchers and because it allows for extremism in the ideal points it estimates, it is the obvious choice for me.
I now turn to the question of which issue areas I should analyze. I did a survey of the political behaviour literature on which issue domains researchers have analyzed. Two obvious choices are economic issues and morality, which are analyzed universally by all American political behaviour studies (Layman and Carsey (2002), Ansolabehere, Rodden, and Snyder (2008), Goren (2012), and Klar (2014)). Other studies-for example, Layman and Carsey (2002) and Conover and Feldman (1981)-include a race dimension. Goren (2012) includes a military strength dimension. I am less convinced that this issue dimension is an important one in American politics on a regular basis. To determine which ones are relevant enough to be included in this paper, I do an exploratory factor analysis (EFA) which I explain in more detail in the Supplementary Information.

Different conceptualizations of polarization
The other problem with the Fiorina-Abramowitz controversy is their disagreement over what constitutes a polarized society. Thus, given some generic policy scale and a distribution of ideal points along it, how does one determine if the society is polarized or not? Abramowitz (2010) presents Figure  1 as evidence that Americans are polarized because the 2004 distribution is more dispersed than the 1984 one. But Fiorina might look at these same graphs and conclude that Americans are not polarized simply because there is no clustering at the poles (most people are in the middle for both years). Alternatively, Abramowitz might argue that Fiorina is not actually observing minute changes over time in Figure 2. One can quickly see that they are using different conceptualizations of polarization. Abramowitz is operationalizing polarization as a change in the distribution over time and Fiorina as a state of the world. As other scholars such as Campbell (2016) have noted, these definitions are not necessarily contradictory but rather different in very nuanced ways. A distribution of ideal points can become more dispersed over time without actually becoming bimodal. Noel (2014, 165-170) notes that there are four main definitions of polarization which scholars use: increased dispersion, growing constraint, growing difference between groups, and bimodality. Hetherington (2009, 431) adds a subcategory of bimodality: clustering at the poles (the extreme ends of the range of the ideology measure). Since I am studying societal polarization, the relevant ones for my paper are growing dispersion and bimodality (I have argued above that constraint is not a good measure of polarization). Finally, in addition to analyzing these two definitions, I will analyze my own definition of polarization which is consistent extremism. Thus, I will investigate if extreme ideologues are a significant proportion in the American public. This definition of polarization may seem like it is just another form of constraint, but it is not. Constraint disallows extremism in its measure whereas my definition specifically captures extremism.
There are scientific methods for studying how dispersed a distribution is. Researchers such as DiMaggio, Evans, and Bryson (1996) have used kurtosis and skew. Lelkes (2016) has used the bimodality coefficient: a scientific measure for how bimodal a distribution is. I will utilize all three in this paper. Because the reader will probably not be familiar with these measures, I have done some simulations in Figure 4 so that the reader can get a sense of all three. The top two distributions are Gaussian with the same mean but different variances. Although it would take too long to discuss all of the details of this simulation exercise, a few things are worth pointing out. One can see that kurtosis becomes more negative as the distribution grows fatter in the tails. The skew measure is positive if the distribution is positively skewed and negative if it is negatively skewed. The bimodality coefficient runs from 0.331 in the most centrist distribution to 0.889 in the most bimodal distribution. This should give the reader some reference when interpreting these values.
Kurtosis, skew, and bimodality can all be studied both over time and as a state of the world. To study them over time, one simply needs to obverse the time series of each. However, to determine if the distribution is polarized in any particular year is harder. For bimodality, the usual standard is 0.56 (Lelkes 2016, 396). But one needs to be careful with using this cutpoint. Take, for example, Simulation 3 in Figure 4. The bimodality coefficient for this distribution is 0.556; just under the threshold for bimodality. But one can certainly see that it is much more dispersed than Simulation 1. This serves to show that the evaluation of polarization as a state of the world must be much more nuanced. Instead of relying on cutpoints, the researcher should describe the state of polarization. Visual evaluation of the distribution is the most powerful tool that the researcher possesses until we can find a better and much more agreed upon measure of polarization.
Estimation of ideal points using confirmatory factor analysis How many issue dimensions are there in American politics? This question does not get enough attention in the polarization literature. To answer this, I do an EFA, but I put it in the Supplementary Information since it is a very discursive analysis (it takes about 13 pages). In the end, I determine with a high level of confidence that there are three important dimensions in American politics (economics, race, and morality). As I hypothesized above, the military strength variables do not load well on any of the dimensions.
With all of the questions which I have described in the Supplementary Information, I pool all the presidential years since 1988 with the exception of 1996. This is due to the fact that all of the racial resentment variables were not asked in this year. Hence, this would be a large gap in the data. However, the loss of this year does not cause too much disturbance to the time series. Hence, it is a reasonable decision to eliminate it. By pooling all of the data together, a respondent in 1988 can be directly compared to a respondent in 2016.
I estimate two different measurement models. The first model has all of the variables loading into a single latent variable (one ideological dimension). The second model has all of the economic, race, and morality variables loading onto their own latent variables. The models fit well: SRMR is 0.087 for the single-dimensional model and 0.065 for the multidimensional model. Because the methods used to evaluate CFA are quite extensive, I leave this to the Supplementary Information.
One might notice that all of the factors load very well onto a single-dimensional model as well. This might be taken as evidence that ideology in America is unidimensional and not multidimensional. To determine if the multidimensional model is better than the one-dimensional model, I do a χ2 difference test-following Layman and Carsey (2002). Table 1 shows that there certainly is a statistical difference between the two models. Since both the Akaike Information Criterion and the Bayesian Information Criterion are both statistically lower for the multiple dimension model than the onedimensional model, the evidence is clear that using the multidimensional model is best. However, perhaps political scientists are arguing over a false dichotomy. It could be the case that Americans think about ideology on both a single left-right dimension and also on issue dimensions. As such, I report the distribution for the single-dimension model in the Supplementary Information.

Analysis of the distributions
The top picture of Figure 5 shows the distribution of the economics variable for the years 1988 and 2016. It should be fairly obvious to the reader  that both of these distributions have strong central tendencies. Figure 7 shows that the economics variable has experienced increased dispersion since 1988 (especially after 2008) in both kurtosis and bimodality. But this increased dispersion hardly amounts to Americans being polarized on economic issues. The kurtosis is −0.53, which is very small according to Figure 4. The level of bimodality is below 0.38, which according to Simulation 1 in Figure 4 is very low. Hence, the Fiorina, Abrams, and Pope (2011) statement that most Americans are closely divided is correct when it comes to economic issues. The bottom picture of Figure 5 shows that Americans were centrally located on race in 1988. One can see that the distribution is significantly different in 2016, there are many fewer people in the centre. There are slightly more racial conservatives in the distribution, but there are many more racial liberals. In particular, there is a nontrivial amount of people who are on the extreme left end of the distribution. Figure 8 shows that the tails of the distribution have grown fatter (kurtosis has decreased) and the distribution has become more bimodal over time. Note that the point where the bimodality coefficient starts off in 1988 is where it ends for the economics coefficient. It went down in 2008 but has sharply increased since then. The skew was highly negative, but this has decreased in recent years. In summary, Americans have become more divided on race than on economics since 1988, but they still remain largely centrist on this domain.
One can see in Figure 6 that in 1988 the distribution on morality was centrally located. There has been a great liberal shift since then with the whole distribution moving leftward. Nevertheless, most people are still centrally located, just more towards the liberal side. Figure 9 shows that the distribution has technically never met the definition of a bimodal distribution of 0.55. In summary, Americans have become much more polarized on morality since 1988 with many more liberals.

Consistent extremists
How many consistent extremists are there in the ANES data? These are people who are dogmatic and extreme about being either liberal or conservative on each issue. Thus, given the chance, these people will tend to mark the most extreme case of the question when answering these surveys. If many people are polarized as in the Tim-Kate scenario that I presented in Figure 3, then we should observe a large amount of these extreme ideologue types in the data with just these three issues. I operationalize a person as a consistent extreme liberal if that person is in the leftmost 10th percentile of the economics, race, and morality variables and a consistent extreme conservative as a person who is in the rightmost 10th percentile in all these variables. I consider this a relatively low bar for extremism. In 2016, there are only 178 extreme left ideologues (4.17% of the total respondents) and only 76 extreme right ideologues (1.78% of the total respondents). Thus, extreme ideologues make up only about 5.95% of all respondents, and the 2012 data is consistent with this result. This is a very small fraction of the population. I vary the cutpoint in the Supplementary Information and find a similar result. Thus, despite some of the political science literature and most of the media pundits talking about how America is a very polarized country, I find evidence to the contrary. Even with this relatively low bar, most Americans are not like Tim and Kate in Figure 3, but rather most Americans are like Bob, Bea, or Ana. They are moderate in their political opinions or they have a mix of both liberal and conservative opinions. The implication is that the situation could get a lot worse than it is right now.

Conclusion
I began this paper by pointing out that the different conclusions in the literature on political polarization is not good for political science. If we are to have credible research results, we must go back and continually evaluate the data and the methods used until we reach a point of consensus. If we do not, then this presents political science as having a lack of coherence-especially when two of the main authors in the debate (Fiorina and Abramowitz) analyze the exact same data and come to completely different conclusions. I deconstruct the underlying assumptions of these two authors and then add two innovations that the political science literature has given us to the analysis. First, instead of assuming that Americans have a single ideal point on a unidimensional ideology scale or instead of assuming that they have an ideal point on every single question that is asked of them on a survey, I assume that Americans have predispositions in high-level issue areas. I then estimate ideal points on three of them: the government's role in economic affairs, race, and morality. I give evidence that Americans do indeed have multidimensional preferences. Second, I apply the insight that societal polarization can both be defined as a state of the world in which the distribution is bimodal and it can also be defined as increasing dispersion over time. This is something that most of the literature on polarization- Campbell (2016) and Lelkes (2016) are exceptions-fails to recognize; they simply assume that everyone will accept what polarization means.
There have been studies done analyzing mass polarization (Campbell 2016;DiMaggio, Evans, and Bryson 1996;Fiorina and Levendusky 2006a;Kinder and Kalmoe 2017;Levendusky 2009), but these studies have usually only used individual issue questions in their analysis. There have been polarization studies done using issue domains (Layman and Carsey 2002;Lelkes 2016;Wood and Jordan 2017), but these studies are usually done analyzing partisan polarization and not mass polarization. Goren (2012) studies both societal (not just partisan) preferences and issue domains, but he does not look at the change in ideal points over time-which is understandable since his book is not about polarization. Furthermore, he only studies two of the three major issue domains in American politics. This paper is the first to study the main issue domains for mass polarization over an extensive period of time in the literature on polarization.
When I evaluate the distributions of these three issue areas using these definitions of polarization, I arrive at a very nuanced conclusion rather than a simple yes/no answer to the research question. First, all of the distributions have experienced increased dispersion over time since 1988. Hence, Americans have become more polarized over time (although to varying degrees). There has been little change on the economic dimension. The race dimension has experience significant dispersion on both sides of the distribution, but there are many more people on the extreme left. The morality dimension has experienced a large shift leftward. Second, I find that none of the distributions are bimodal. Thus, Americans are not polarized according to this definition. Finally, I find very few people who have an extreme ideology (either liberal or conservative) in all three of these issues. Even if a person is on the extreme end of the distribution of one of the issues, she is likely to be in the middle or even on the other side on one of the other issues.
In summary, people have become more polarized over time since the 1980s, but that does not mean that they are deeply divided. America is certainly not the highly polarized society that many media pundits and even some political scientists want to portray it as. In short, it could get much worse than it is right now. If American politics seem polarized right now, one can imagine what it would be like if this process of polarization continues.

Disclosure statement
No potential conflict of interest was reported by the author(s).