Depolarizing on Gay Rights Issues over Time

E_o: No trend in the consensus measure over time or a decline in consensus over time.

E_a: Consensus increases over time.

Conflict Expectations

Polarizing on Gay Rights Issues over Time

E_o: No trend in the consensus measure over time or an increase in consensus over time.

E_a: Consensus decreases over time.

Consensus Measure (CM)

In order to conduct analysis of the consensus and conflict trends in public attitudes on gay rights in Chapter 5, the categorical responses must be converted to a single measure. The GRD consists of frequency percentages across the polling question categories, not the individual responses that make up those percentages. The observational unit for the GRD is the poll and not the respondent. While it is possible to work backwards from the N and frequencies to produce means and standard deviations (something I do for a select number of polls), it is ultimately unnecessary to assess polarization of political issues (i.e. gay rights). We can examine the trends in gay rights attitudes in terms of consensus and conflict with a few manipulations of the available data. Conceptually, I define absolute conflict as a 50 / 50 distribution across the Anti-Gay and Pro-Gay categories. Implicitly, absolute consensus is where 100 percent of the respondents fall into either the Anti-Gay or Pro-Gay categories. Figure 4.2 illustrates the three-step process to producing a measure of consensus (or the absence of it).

We start with the binary categories for the Anti-Gay and Pro-Gay attitudes in the American public. Figure 4.2 has four hypothetical attitude distributions, ranging from near-absolutely consensus (95 to 5) to near-absolute conflict (55/45). The first step is to convert the category percentages to deviations from 50 percent (absolute conflict). Note that this conceptualization of absolute conflict is consistent with the theoretical arguments on polarization developed in Chapter 3 and is consistent with the group polarization measure I developed there (and discuss in empirical terms in Section II). Absolute conflict is defined as society divided into two oppositional groups of equal size. While the measure itself only permits two groups and the distance between the groups is fixed, this measure captures the size of the ‘pro’ side relative to the size of the ‘con’ side. If an issue is in a state of consensus, then we’d expect a high percentage of society to fall on one side of the issue or the other. If the issue is representative of a salient political conflict, however, we would expect opinion to be divided relatively equally (and absolutely equally in the limit). In Figure 4.2A, we have a hypothetical rendering of four sets of responses on four different aspects of the gay rights issue. These could be, for example, gays in the military, gay marriage, gay adoption, and gay inheritance. For illustrative purposes, the distributions are quite distinct: The first gay rights issue is near consensus, while the last is at near absolute conflict. In Figure 4.2B, the Anti-Gay and Pro-Gay categories for each of the distinct questions on gay rights are represented in terms of their distance above and their distance below the 50 percent baseline. Poll Question C2 illustrates why one cannot simply choose one of the categories and use it in the

Figure 4.2: Creating a Measure of Consensus


Figure 4.2A: Four Binary Variables



Figure 4.2B: Variable Categories Relative to 50 Center-point



Figure 4.2C: Absolute Value of Category Deviation from 50



Figure 4.2D: Combined Consensus Measure

polarization models. The Anti-Gay and Pro-Gay categories for C2 do not sum to 100%. This is actually a frequent occurrence in the GRD. There are categories like “not sure” or “don’t know” that cannot be collapsed into one of our two substantive categories. Furthermore, there are middle categories (neither approve nor disapprove) that should not be merged into one of the two categories. Thus, t his measure is necessary as a consequence of the fact that, even with the collapsed categories, the Anti-Gay and Pro-Gay category frequencies can and do add up to percentages below 100 percent. Only 27 of the 689 polls have Anti-Gay / Pro-Gay categories that sum to 100 percent. Since the deviation from 50 percent in the Anti-Gay category does not mirror the deviation from 50 percent in the Pro-Gay category, the consensus measure must combine the two for an aggregate measure across the two categories.

Once you have calculated deviations from 50 percent for both categories, the seconds step (Figure 4.2C) is simply taking the absolute value of those deviations. This leads to the third and final step of combining the two deviations into a single, composite consensus measure. As can be seen in Figure 4.2C, this consensus measure is a valid and reliable measure of the combined deviations from absolute conflict for the Anti-Gay and Pro-Gay categories. A consensus score of 100 represents absolute consensus, and a consensus score of zero represents absolute conflict. The measure, henceforth referred to as CM, is thus ready for comparison across years and inclusion in the polarization trend regressions.

Mean, Dispersion, and Bimodality Measures of Polarization

For the GSS data (and selected polls) in Chapter 5 and the closed-ended items from the ANES in Chapter 6, I examine not only trends in consensus and conflict but also the extent to which public opinion on gay rights have become more dispersed on average over the time series. The dispersion measures are also useful in assessing changes on gay rights attitudes within and between the parties. I employ a measure of bimodality (kurtosis), a measure of average position (mean), and two measures of dispersion (standard deviation and coefficient of variation) to assess the degree that American public opinion on gay rights has fractured over the past 35 years.

Since polarization can occur independent of changes in the mean, shifts in the mean on an issue dimension to the extremes can reflect consensus while shifts to the center can reflect an increase in conflict over an issue. However, for the most part, the variables included from the ANES in the Chapter 6 analysis are already a subject of conflict over the course of the time series. There is no consensus on ideology, defense spending, or jobs in the United States. We may see an emerging consensus, however, on attitudes towards minorities and women. Generally speaking with political variables, an increase in the mean which moves the mean to one extreme or another is an indication of consensus and not conflict.

This is the especially the case with affect measures such as thermometer scores. An average affect score of 50 is likely not the result of almost every respondent giving the group, party, or candidate a score in the middle of the scale. Rather, it is likely the consequence of a sizeable number of respondents giving scores in the sixties and seventies with an equal portion of respondents giving scores in the forties and thirties. Likewise, an average affect score of 70 suggests that most respondents have very positive feelings towards the group, party, or candidate and hence there isn’t a great deal of room for conflict in the related issue dimension (if there is one). However, likelihood is not empirical certainty, and hence any interpretation of changes in the mean (if there is one) must be assessed in terms of the distribution of the variable prior to the change and the distribution afterwards. A failure to account for the distribution of opinion on the group makes the means ultimately uninterpretable in terms of polarization or depolarization. Where there is a reasonable spread of opinion on a group or issue, movements in the mean over time (if they occur) can be understood as moves towards consensus or conflict depending on the starting point (year) and whether opinion is moving closer or further away from the extreme of the scale the previous average was closest to. Hence a move from 65 to 75 is a move towards (rather than away from) the pole the mean is most proximate to and hence indicates increasing consensus. A move from 65 to 55 would be a move away from that poll and hence indicates conflict. The trend model assesses changes in the average position on the issue or group over time. Whether a negative or positive coefficient is indicative of polarization is dependent upon whether the pole that the mean opinion is proximate to is located higher or lower on the scale.

Equation 4.2: Mean Model

E_o: No trend in the mean position.

E₁: A significant trend towards the pole the average issue position is proximate to. (depolarization)

E₂: A trend in the mean issue position away from the pole the average issue position is proximate to. (polarization)

The principle of bimodality is intended to capture the level of conflict within society by assessing the degree to which opinion on an issue or attribute is divided into two camps (see Chapter 3). A measure which validly and reliably assesses the bimodality principle must capture the degree to which a distribution is located at one, two, or multiple modes and be sensitive to changes in that distribution. If the population is divided into two camps on an issue, then that would tend to increase identification (between those who share the same views) and increase perceptions of alienation (between those who do not share the same views). While the sizeable number in opposition may increase the necessity for making compromises (given majoritarian American political institutions), the separation into two camps makes such compromise more difficult and enhances conflict between the two groups as neither side can be dismissed as irrelevant or incapable of securing political outcomes (as, say, small fringe groupings can be).

As noted previously (see Chapter 3), a rough approximation of bimodality for a distribution is captured in the fourth moment around the mean (standardized) otherwise known as kurtosis. This measure provides an approximation of the ‘peakedness’ of the distribution. I’ve noted some of the problems with using kurtosis to measure bi-modality. As a measure of peakedness, kurtosis is a rough approximation rather than a direct measure of bimodality. While bimodal distributions are less ‘peaked’ than normal distributions, differently shaped distributions present special problems for kurtosis and thus the fourth moment about the mean is at best a rough approximation of bimodality. Fine differences in bimodality between certain non-normal distributions may produce inconsistent changes in kurtosis. That said, kurtosis is strongly correlated with bimodality, as demonstrated in Chapter 3. The kurtosis measure is thus useful in distinguishing between bimodal distributions and less-bimodal distributions on the whole.

Kurtosis is used here to measure the change in the shape of the distributions of issue dimensions overtime.

Equation 4.3: Kurtosis

As kurtosis = 0 is centered on t he normal distribution, kurtosis scores which fall below zero are indicative of a more bimodal distribution than the normal distribution (higher values connote a unimodal or single-peaked distribution). With respect to a trend over time, a negative trend in kurtosis indicates a shift towards bimodality in the distribution (conflict), while a positive trend indicates a shift towards unimodality (consensus). This trend is modeled with the average kurtosis in a given year on an issue serving as the dependent variable with survey year as the independent variable.

Equation 4.4: Bimodality Model



Bimodality of Issue Dimensions Expectations

E_o: No trend in the kurtosis of the distribution.

E₁: A significant positive trend in the kurtosis of the distribution (depolarization).

E₂: A significant negative trend in the kurtosis of the distribution (polarization).

The interpretation of results for the dispersion measures is relatively straightforward. In order to measure dispersion, we need a measure that both reflects the relative distance that individual respondents differ from one another as well as taking into account the proportion of opinion located in the extremes relative to the center of the distribution. Increased dispersion indicates polarization as it reflects an increase in the distance between individuals and/or groups within society on that issue or attribute. If opinion is highly dispersed, then institutions and actors which seek to compromise on policy related to that opinion may find it difficult or impossible to get the requisite support at the popular level. Conversely, a constrained distribution of opinion (low dispersion) suggests a policy space ripe for compromise and perhaps even consensual politics. The standard deviation is a measure of the dispersion in the data. As such it is a good measure of the degree to which consensus on gay rights attitudes, abortion attitudes, economic issues attitudes, defense policy attitudes, etc. exists at the mass level and how that consensus has changed over time.

The traditional measure of dispersion is variance, or its standardized version: the standard deviation. As opinion dimensions become more polarized, variance (and thus the standard deviation) should increase.

Equation 4.5: Standard Deviation

An increase in the standard deviation on an issue indicates that mass public opinion on the issue has become more polarized on that issue. The more dispersed the population, the more likely the issue will produce intractable political conflict rather than centrist / moderate compromise polices. A more dispersed opinion distribution means that, in order to produce a compromise policy, citizens must agree to a change in the status quo that is, on average, further distant from their own ideal point. This increases conformity costs in the creation of public policy on the issues where we observe greater dispersion. This trend is modeled with the average standard deviation in a given year on an issue serving as the dependent variable with survey year as the independent variable.

Equation 4.6: Bimodality Model



Dispersion Expectations on Issues

H_o: No trend in the standard deviation on issues

H_a: A significant decrease in the standard deviation on issues (depolarization).

H_a: A significant increase in the standard deviation on issues (polarization).

For the Republican and Democratic likes and dislikes, I create conservative and liberal response sets for the government philosophy, social, economic, and defense issue dimensions. The categorization of the open-ended response sets is reported in Table 5.1. Note that the expected applicable response set is dependent upon whether it is a “like” or “dislike” variable. In this analysis I combine the conservative and liberal responses on the party likes and dislikes to get measures of the total number of social issue mentions (as well as mentions on the other kinds of issues).

In assessing the open-ended responses here, I will be looking for a trend in the number of issue mentions across the time-series. For example and relevant to the culture wars thesis, if the number of social issue mentions as an “important national problem” or as a reason to like or dislike the two political parties have increased over the past three decades, then that is evidence suggesting an increase in the salience of the issue dimension (and thus evidence it is a dimension on which politically relevant polarization can occur). Furthermore, if social issue-mention trends deviate along party lines, then it would be evidence of partisan polarization and the increasing importance of social issues in political competition. For example, if citizens increasingly mention social issues as the reasons they like or dislike the parties then this would be evidence supporting the culture wars thesis and evidence suggesting partisan polarization on the social issues. This trend is modeled by regressing year on the total number of issue mentions for a survey year in the party likes and dislikes item as well as the national problems item.

Equation 4.7: Frequency Polarization Model



Issue Mention Expectations

H_o: No trend in the frequency of issue mentions on this dimension

H_a: A significant negative trend in the frequency of issue mentions (depolarization).

H_a: A significant positive trend in the frequency of issue mentions (polarization).