Disambiguation of social polarization concepts and measures

ABSTRACT

This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena.

KEYWORDS:

• Belief aggregation
• formal epistemology
• measurement
• polarization
• social epistemology

Notes

¹ Furthermore, increasing the number of dimensions also expands polarization into additional distinct senses; i.e., there are types of polarization (such as the correlation of attitudes across multiple issue dimensions (Baldassarri & Gelman, 2008; Fiorina et al., 2010)) that are only sensible for higher-dimensional data.

² Specifically, we provide measures that operate on a metric space so that there is a clear ordering from one end to the other and that distance measures are well-defined everywhere.

³ Our approach here is a naive approach that simply calculates the number of modes as one plus the number of local minima. In the data analysis presented in Section 6 we find cases in which the peak and valley differ only by a few responses, but this is sufficient to reveal an additional group. Such cases may be better captured with a measure that puts minimal variation restrictions on the distribution and/or counts partial groups based on the variation (see Section 5 for more ideas on combined and hybrid measures). Another alternative is to find endogenous groups according to halo-like technique that connects bins together into groups as long as they are sufficiently similar (Mas, Flache, & Helbing, 2010).

⁴ In applications to higher-dimensional data, endogenously defining the groups requires finding the manifolds of the distribution—a well-defined, but much more complicated, similar procedure.

⁵ Even in the case of measuring the number of groups, the task is more complicated for network and spatial data. Take, for example, the various algorithms for detecting community structure (and hence the number of communities) in networks. Those network connections only reflect part of the story, and a measure of polarization on networks must combine the community structure of the agents with their attitude values into a single polarization measure.

⁶ To visualize how this works, look at Figure 7 (a) and trace along the minimum of the two distributions from left to right. The sum of those heights will be the area of the gray region, which is then normalized by the total population (the size of A plus the size of B).

⁷ This is one of the boundary condition caveats: If both spread and coverage were 100% of a bounded region, then decreasing spread would imply a decrease in coverage, although the reverse is not true.

⁸ This is a second boundary condition caveat: If each bin initially only has one occupant then moving occupants to increase spread without changing dispersion may be impossible.

⁹ The discrepancy occurs when multiple “islands” of agents coincidently possess all the same traits values.

¹⁰ Specifically, our technique requires ordered response values rather than categorical responses and excludes responses of “no response,” “don’t know,” “can’t choose,” and the like. Some questions (like POLVIEWS described below) ask participants to rank themselves on a 1-7 scale. These variables can be analyzed without analytical gymnastics across multiple variables. The ABORTION variable we use is, however, a composite of multiple true/false questions that are added together to produce a 0-8 scale.

¹¹ For the political views data taken together, no bins are empty. When broken down by BIBLE, in 1984 there are no respondents who chose extremely conservative and answered that the bible is a book of fables – and that is the only empty bin. For the abortion analysis below, there are a few scattered empty bins for the book of fables group, likely the result of low sample size in some years. They are left out of the analysis because they do not indicate coherent patterns in the data.

¹² A regression analysis between the community fragmentation measure and the year naturally reveals a positive relation with high confidence, but with so few samples (18 years) and a single variable this is not an appropriate characterization of coherent patterns in the data.

¹³ There are cases, for other questions, in which some response values are not given by anybody for some years. If these questions are used to exogenously define groups, then the number of groups will change across time. As mentioned earlier, this is rare for survey data, but when analyzing simulation models it is common for predefined types of agents to enter and leave the population.

¹⁴ Because the GSS data used here are not from longitudinal studies, we are not detecting individuals changing their religiosity, but just a reflection of changes in the cross section of social attitudes.

¹⁵ One must resist the inclination of assigning a negative connotation to polarization in the interpretation of these results. Here polarization is a purely descriptive term. It may very well be beneficial to have equal numbers of people in each group in some cases, and everybody in one group for other cases. The context determines whether high or low polarization values are desirable.

¹⁶ Specifically, the ABORTION variable used here is aggregated by COMPUTE from the study /html/D3/GSS12 and reported by the SDA tool (Thomas, 2013) as the sum of ABDEFECT, ABNOMORE, ABHLTH, ABPOOR, ABRAPE, ABSINGLE, and ABANY (Smith, Marsden, Hout, & Kim, 2013). First we analyze the ABORTION variable by year filtered by BIBLE, and then grouped exogenously by BIBLE (paralleling our analysis of POLVIEWS above). The composite ABORTION variable has response positions ordered from more liberal to more restrictive, whereas the POLVIEWS had seven.

¹⁷ The attitude of this group fluctuates only slightly around its mean value of 0.1819 on a 0 to 1 scale in which higher numbers are more anti-abortion.