Disambiguation of social polarization concepts and measures

May combine two claims.

In the early 1970s, both Senators and Congressmen voted along party lines about 65% of the time; in the early 2000s, that had increased to over 85%.

“In the early 1970s, both Senators and Congressmen voted along party lines about 65% of the time; in the early 2000s, that had increased to over 85% (McCarty et al., 2008).”

• cites McCarty et al., 2008Partly supported

  The Abstract describes a shift toward more divisive politics beginning in the mid-1970s, and “Insert Figures 3 and 4 About Here” says the parties’ positions moved apart in both chambers. Our copy does not give the claimed 65% and over-85% rates of voting along party lines; its near-90% figures refer instead to how well a spatial model classifies votes. (LLM, conf=0.82)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The trend in attitudes toward abortion is not strong.

“Although we will later see that the trend is not strong, it is the case that attitudes toward abortion between 1970 and 1990 (shown in Figure 1) reflect high levels of polarization in the sense of distinctness because few individuals hold positions between the two large groups.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In Figure 5(a), the subdistributions on the left are clustered together and as a result the distribution is less polarized than in (b) when they are not.

“What this diagram makes clear is that in (a) the subdistributions on the left are clustered together and as a result the distribution is less polarized than in (b) when they are not.”

May combine two claims.

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.

“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.”

Classified as probably not a substantial claim. May combine two claims.

The paper's formal measures up to this point either ignore groups completely or focus on in-group aggregates and comparisons of group means.

“Our formal measures up to this point either ignore groups completely or focus on in-group aggregates and comparisons of group means.”

May combine two claims.

Group divergence value in 1984 is 0.1170, and in 2012 is 0.1774; the rise is not monotonic, but only two years prior to 1996 reached above 0.12, while every year after 1996 scored above 0.12.

“The value in 1984 is 0.1170, and the value in 2012 is 0.1774; although the rise is not monotonic, it is the case that only two years prior to 1996 reached above 0.12, while every year after 1996 scored above 0.12.”

May combine two claims.

In 1996, the proportion of respondents who described themselves as strictly conservative increased from 16.3% to 18.4%, putting that bin above the proportion who described themselves as slightly conservative (which went from 16.6% to 16.7%), creating a new peak at the conservative bin.

“in 1996 the proportion of respondents who described themselves as strictly conservative increased from 16.3% to 18.4%, which put that bin above the proportion who described themselves as slightly conservative (which went from 16.6% to 16.7%) creating a new peak at the conservative bin.”

May combine two claims.

Group consensus reveals a more consistently downward trend, but the difference in values is too small to make any conclusions.

“Group consensus reveals a more consistently downward trend, but the difference in values is too small to make any conclusions.”

May combine two claims.

In 2012 the single group divide is at the bin representing slightly liberal, and the conservative and moderates are all in a group together.

“In 2012 the single group divide is at the bin representing slightly liberal, and the conservative and moderates are all in a group together.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In some years the number of respondents is fewer than 700 (in weighted terms), while in other years it is greater than 2,000.

“In some years the number of respondents is fewer than 700 (in weighted terms), while in other years it is greater than 2,000.”

May combine two claims.

The actual number of mode-defined groups for abortion opinions is consistently three (except in 1990 when there are four and in 2008 when there are two), but the locations of the minima that separate these groups constantly change locations.

“The actual number of mode-defined groups is consistently three (except in 1990 when there are four and in 2008 when there are two), but the locations of the minima that separate these groups constantly change locations.”

Probably not a substantial claim: may not pass S4 (based).

The overall population is not appreciably drifting apart as measured by population dispersion and group divergence.

“the overall population is not appreciably drifting apart (as measured by population dispersion and group divergence)”

May combine two claims.

Although there were sometimes two and sometimes three groups after 1996, there is no clear increasing or decreasing pattern in the number of groups.

“Although there is sometimes two and sometimes three groups after 1996, there is no clear increasing or decreasing pattern.”

May combine two claims.

The number of endogenously defined groups, as well as the measures across those groups, undergo a striking and lasting shift in 1996.

“The number of endogenously defined groups, as well as the measures across those groups, undergo a striking and lasting shift in 1996”

May combine two claims.

When strictly measured, the number of modes in the abortion data is only equal to two in a single year; the data are not bimodal.

“when strictly measured, the number of modes in the data is only equal to two in a single year: strictly, speaking, the data are not bimodal.”

May combine two claims.

Distinctness went from a high of 0.7175 in 2002 down to 0.6548 in 2012, meaning that there was an 8.68% increase in the average amount of overlapping responses among the groups.

“Distinctness went from a high of 0.7175 in 2002 down to 0.6548 in 2012, meaning that there was an 8.68% increase in the average amount of overlapping responses among the groups.”

May combine two claims.

From 1996 to 2010 there is a group divide at slightly conservative, and the size parity jumps when a third group also forms (in 2000, 2008, and 2010).

“From 1996 to 2010 there is a group divide at slightly conservative, and the size parity jumps when a third group also forms (in 2000, 2008, and 2010).”

May combine two claims.

For the POLVIEWS political views data, population dispersion climbs slightly, but not monotonically, from 1984 to 2012, a slow and steady increase despite abrupt changes in the shape of the distribution picked up by other measures.

“The population dispersion climbs slightly, but not monotonically, from 1984 to 2012”

• Also stated in: § 6.1. Political polarization · plain

  “The population dispersion experiences a slow and steady increase despite the abrupt changes in the shape of the distribution picked up by other measures.”

• AssumptionRests on an assumption: The POLVIEWS 1-7 scale validly measures general political views.

May combine two claims.

Within the timespan for which groups are observed (1996-2012), group divergence, distinctness, consensus, and size parity do not consistently change, so the only sense in which the population polarized is community fragmentation.

“group divergence, distinctness, consensus, and size parity do not consistently change, so we have just one sense in which the population polarized: community fragmentation.”

May combine two claims.

Community fragmentation has a constant value of three for the exogenous analysis, but reveals the greatest change in polarization for the endogenous case.

“This variable has a constant value of three for the exogenous analysis, but reveals the greatest change in polarization for the endogenous case.”

May combine two claims.

The Inspired Word group experienced an up-swell between 1994 and 2008, keeping it roughly in the middle.

“The Inspired Word group experienced an up-swell between 1994 and 2008, keeping it roughly in the middle.”

May combine two claims.

As a result of the moving valleys, the responses included in each group are constantly shifting, and this produces volatile group-based measure values.

“As a result of the moving valleys, the responses included in each group are constantly shifting, and this produces volatile group-based measure values.”

May combine two claims.

In the abortion-by-religiosity analysis, there are no stark trends, and only divergence reveals sharply erratic patterns.

“Again there are no stark trends, and only divergence reveals sharply erratic patterns.”

May combine two claims.

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.

“When broken down by BIBLE, in 1984 there are no respondents who chose extremely conservative and answered that the bible is a book of fablesand that is the only empty bin.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

For political views there was just one mode until 1996, with demarcation lines highly consistent afterward.

“For political views there was just one mode until 1996, with demarcation lines highly consistent afterward.”

May combine two claims.

Along with that change, the group sizes are becoming more equalized; fewer individuals take the Bible literally and more consider it a book of fables, although the latter remains the smallest group.

“Along with that change we see the group sizes becoming more equalized; fewer individuals take it literally and more consider it a book of fables (although the latter remains the smallest group).”

May combine two claims.

The population dispersion shows a slight increasing trend, although the magnitude of the increase is too small to make any claims of significance.

“The population dispersion does show a slight increasing trend, although the magnitude of the increase is too small to make any claims of significance.”

May combine two claims.

The shifting third group (sometimes between the two dominant groups and sometimes at the far conservative side) is always small (typically less than 10%), but the size parity measure still consistently scores around 90%.

“The shifting third group (which is sometimes between the two dominant groups and sometimes at the far conservative side) is always small (typically less than 10%), but the size parity measure still consistently scores around 90%.”

May combine two claims.

Size parity is similar for the two datasets-staying in the high 80s and low 90s-although the political views data are more volatile.

“Size parity is similar for the two datasets-staying in the high 80s and low 90salthough the political views data are more volatile.”

May combine two claims.

In the abortion-by-religiosity analysis, the population dispersion is unchanged, and the group size parity is the same as in the POLVIEWS analysis because the exogenously defined groups are identical.

“Naturally the population dispersion is unchanged, and the group size parity is the same as in the POLVIEWS analysis because the exogenously defined groups are identical.”

May combine two claims.

The across-time average group divergence for abortion is nearly three times the group divergence for political views (0.3715 versus 0.1307), but groups in both data have similar concentrations around their means (average consensus is 0.5564 versus 0.5985).

“The across-time average group divergence for abortion is nearly three times the group divergence for political views (0.3715 versus 0.1307), but groups in both data have similar concentrations around their means (average consensus is 0.5564 versus 0.5985).”

May combine two claims.

Although views on abortion are cleanly separated at the population level, when broken down by religious categories they are actually less polarized in the senses of consensus, divergence, and distinctness but not of size parity.

“Although views on abortion are cleanly separated at the population level, when broken down by religious categories they are actually less polarized in the senses of consensus, divergence, and distinctness but not of size parity.”

May combine two claims.

The exogenous analysis reveals that increasing religiosity correlates well with increasingly conservative political views, but that the mean positions of these three groups have been slowly diverging.

“the exogenous analysis reveals that increasing religiosity correlates well with increasingly conservative political views, but that the mean positions of these three groups have been slowly diverging.”

May combine two claims.

The intergroup positions for political views were largely consistent even as the number changed, but the demarcation lines were constantly in flux for abortion despite the consistent number of groups.

“Also, the intergroup positions for political views were largely consistent even as the number changed, but the demarcation lines were constantly in flux for abortion despite the consistent number of groups.”

Probably not a substantial claim: may not pass S3 (load-bearing).

For the abortion analysis, there are a few scattered empty bins for the book of fables group.

“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.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

Abortion opinion group consensus has a slightly wider range around a slightly higher value of 0.88.

“Abortion opinion group consensus has a slightly wider range around a slightly higher value of 0.88.”

May combine two claims.

The distinctness of endogenous groups is consistently very high (near 95%) for abortion, but consistently near 86% for political views.

“the distinctness of these endogenous groups is consistently very high (near 95%) for abortion, but consistently near 86% for political views.”

May combine two claims.

There are weak trends, but also weak trends of decreasing polarization in some senses.

“There are weak trends, but also weak trends of decreasing polarization in some senses.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

Group divergence is volatile for both datasets: political views toggles between 0.40 and 0.63 depending on the number of groups; abortion tumbles between 0.637 and 0.952 without being tightly coupled to the number of groups.

“Group divergence (normalized distance among group means) is volatile for both datasets: political views toggles between 0.40 and 0.63 depending on the number of groups; while abortion tumbles between 0.637 and 0.952 without being tightly coupled to the number of groups.”

May combine two claims.

There are two dominant peaks, but the distribution of abortion opinions is typically trimodal.

“There are two dominant peaks, but the distribution is typically trimodal.”

May combine two claims.

The paper's polarization analysis found few clear trends for any segment of the data and no strong trends of increasing or decreasing polarization for political views or abortion from 1984 to 2012.

“The result of our polarization analysis is that there are few clear trends for any segment of the data, and no strong trends of increasing or decreasing polarization for political views or abortion from 1984 to 2012.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

The average distinctness of the groups for abortion opinions is 0.7394, and for political views it is 0.6886.

“The average distinctness of the groups for abortion opinions is 0.7394, and for political views it is 0.6886.”

May combine two claims.

The gradual increase in dispersion only amounts to a 5.85% change, and the increase is not monotonic.

“The gradual increase only amounts to a 5.85% change in dispersion, and the increase is not monotonic.”

Probably not a substantial claim: may not pass S3 (load-bearing).

For the political views data taken together, no bins are empty.

“For the political views data taken together, no bins are empty.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

On average there are 2.5% of responses in the bins between groups for abortion and between 5 and 7% for political views.

“on average there are 2.5% of responses in the bins between groups for abortion and between 5 and 7% for political views.”

May combine two claims.

Our preliminary polarization analysis of the DW-nominate data revealed larger and clearer differences for both endogenous and party-defined exogenous groups.

“Our preliminary polarization analysis of the DW-nominate data revealed larger and clearer differences for both endogenous and party-defined exogenous groups.”

Classified as probably not a substantial claim.

The numbers produced by the measures are not informative in isolation; they gain meaning as relative values through comparisons.

“The numbers produced by our measures are not intended to be informative in isolation; rather, they gain their meaning as relative values through comparisons (i.e., being more or less polarized).”

Classified as probably not a substantial claim.

When authors say a system has "become polarized," this means the value for some measure(s) has gone from a low to a comparatively high value, a quantitative increase rather than a qualitative shift.

“A further corollary of our quantitative measurement approach is that when authors say of a system that it has “become polarized” this simply means that the value for some measure(s) has gone from a low to a comparatively high value.That is, it is a quantitative increase rather than being a qualitative shift implying that it possesses a new property.”

Probably not a substantial claim: may not pass S4 (based).

For each of the other measures, an example can be generated that demonstrates its independence.

“However, for each of the other measures here an example can be generated that demonstrates its independence (see Section 4 for more information about measure independence).”

Probably not a substantial claim: may not pass S3 (load-bearing).

The histogram representation can also capture more open-ended questions and household income values through binning or density functions.

“It can also be used to capture more open-ended questions (e.g., “what percentage of the federal budget should be spent on education?”)and household income values through binning or density functions.”

May combine two claims.

The discrete coverage measure does not rely on any distance measure or ordering of the values, and therefore is appropriate for categorical data.

“Note that this discrete measure does not rely on any distance measure or ordering of the values, and therefore is also appropriate for categorical data.”

Classified as probably not a substantial claim.

The measures provided are properties of a distribution that can be captured at any time-slice of the system.

“The measures we provide here are properties of a distribution that can be captured at any time-slice of the system.”

May combine two claims.

The abortion attitude data in Figure 1 are trimodal in most years, with a liberal group, a central group, and a third group on the far conservative side.

“furthermore, in most years there is a third group created by an upturn on the far conservative (right) side.So in this strict sense that data is trimodal and would result in a measure of three groups for most years.”

• cites DiMaggio et al., 1996 sourceNot checked — no full text of the source

Classified as probably not a substantial claim.

Spread and dispersion as defined here are clearly distinct polarization concepts.

“Just being “far apart” is not as precise as it could be because although spread is also a measure of statistical dispersion, spread and dispersion as defined here are clearly distinct polarization concepts.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The scenario in Figure 1 (abortion attitudes) has been identified as a clear case of polarization by DiMaggio et al. (1996) and others.

“The scenario in Figure 1 has been identified as a clear case of polarization by DiMaggio et al. (1996) and others.”

• cites DiMaggio et al. (1996) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The histogram representation naturally captures Likert scale data recovered from surveys and opinion polls.

“This representation naturally captures the Likert scale data recovered from surveys and opinion polls.”

May combine two claims.

Existing formal measures of polarization are often specific to the analyzed dataset or topic, not fully formalized, not evaluated against other measures, or composite of the measures presented here.

“In those cases in which a formal measure is provided (see Christen, Ott, & Schwarz, 2013;DiMaggio et al., 1996;Fiorina et al., 2010;Estaban & Ray 2012), it may be specific to the analyzed dataset or topic of interest, not fully formalized, not evaluated compared to other measures and/or presented as a measure that is a composite of the measures presented here.”

• cites Christen, Ott, & Schwarz, 2013 sourceNot checked — no full text of the source
• cites DiMaggio et al., 1996 sourceNot checked — no full text of the source
• cites Fiorina et al., 2010Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The term polarization is sometimes used to refer to a static property and sometimes to a process.

“The term polarization is sometimes used to refer to a static property and sometimes a process (DiMaggio et al., 1996).”

• cites DiMaggio et al., 1996 sourceNot checked — no full text of the source

Classified as probably not a substantial claim. May combine two claims.

Some particular measures provided will not work for every type of data (e.g., categorical or overly coarse-grained), but they provide clarity on conceptual distinctions and are applicable to histograms from surveys and simulation outputs of models with epistemic agents.

“Although some of the particular measures provided here will not work in capturing the distinct senses of polarization in every type of data (e.g., categorical or overly coarse-grained data), they should provide clarity on the conceptual distinctions and are applicable to two key forms of data: histograms of attitude distributions from surveys and simulation outputs of models with epistemic agents.”

Classified as probably not a substantial claim. May combine two claims.

The formalism for the measures depends only on features of the distribution and not on what the distribution represents, so the properties can be anything that admits cardinal values.

“These properties can be anything that admits cardinal values because our formalism only depends on features of the distribution and not on what that distribution represents.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Identifying groups by local minima precludes subpopulations from overlapping because group boundaries are defined by the local minima in the distributions.

“Identifying groups in this way precludes the subpopulations from overlapping because group boundaries are defined by the local minima in the distributions.”

Probably not a substantial claim: may not pass S2 (checkable).

Because these measures were not as finely defined in their work, their analysis fails to separate the distinct senses.

“That is, because these measures were not as finely defined in their work, their analysis fails to separate the distinct senses.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Coverage is a crude measure of diversity, and there is a linkage between a diversity of attitudes and those attitudes being polarized.

“Coverage is actually a crude measure of diversity, and there is a linkage between a diversity of attitudes and those attitudes being polarized (explored in other work).”

Classified as probably not a substantial claim.

Endogenous distinctness among any number of revealed groups can be calculated via formula (7).

“Endogenous distinctness among any number of revealed groups can be calculated via the following formula:”

May combine two claims.

As the population of each group becomes more focused on a few attitudes, the closer the average distance to the mean is within each group, and the more polarized the population.

“As the population of each group becomes more focused on a few attitudes, the closer the average distance to the mean is within each group, and the more polarized the population (as illustrated in Figure 9).”

Classified as probably not a substantial claim.

The measures below require comparisons among subpopulations or sub-distributions.

“Because the measures below require comparisons among subpopulations or sub-distributions, different group identification methods yield variants of the interpretations and polarizations measures to come.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Republicans have become more consistent on economic and civil rights issues.

“In fact, Republicans have become more consistent on economic and civil rights issues, while Democrats have lost constraint on these issues and become a bit more coherent in their moral views.”

• cites Baldassarri & Gelman, 2008 sourceNot checked — no full text of the source

May combine two claims.

Bartels' analysis of voting behavior and party identification from 1952 to 1996 reveals that the strength and importance of party identification for voting behavior dropped in the 1960s and 1970s and has rebounded through the 1980s and 1990s.

“Bartels' analysis of voting behavior and party identification from 1952 to 1996 reveals that the strength and importance of party identification for voting behavior dropped in the 1960s and 1970s and has rebounded through the 1980s and 1990s.”

• cites Bartels, 2000 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Formula (6) determines the proportion of the overlap of two distributions by normalizing the sum of the values at each bin of whichever distribution has a lower value in that bin.

“This formula determines the proportion of the overlap of two distributions by normalizing the sum of the values at each bin of whichever distribution has a lower value in that bin.”

May combine two claims.

The frequency of individuals at the locations of the parties has increased while the frequency of individuals between them has decreased.

“The frequency of individuals at the locations of the parties has increased while the frequency of individuals between them has decreased.”

• AssumptionThe authors state this as an assumption: The two major U.S. political parties represent positions toward the left and right sides of a spectrum, and at least some independents are between these parties.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The number of groups acts as a distinct sense of polarization.

“While the number of groups acts as a distinct sense of polarization, the group identification methods described above also play a role in the measures that follow.”

May combine two claims.

A normalized entropy measure fits the description of a size parity measure exactly, although for endogenously defined groups this measure may be erratic when the groups change and/or shift boundary bins.

“A normalized entropy measure fits this description exactly, although for endogenously defined groups this measure may be erratic when the groups change and/or shift boundary bins.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

These findings require a multidimensional issue space and a measure of consensus that aggregates for each party how they have changed across all the issues.

“Clearly these require a multidimensional issue space and a measure of consensus that aggregates for each each party how they have changed across all the issues.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

A less elegant measure of the exogenous distinctness of two groups is provided by formula (6).

“A less elegant measure of the exogenous distinctness of two groups (but one that is useful for our intended data from surveys and agent-based models) is provided by:”

May combine two claims.

Any change that increases the distance of the means will increase divergence, which can also be accomplished while holding spread, coverage, distinctness, etc. constant.

“However, any change that increases the distance of the means will increase divergence, which can also be accomplished while holding spread, coverage, distinctness, etc. constant (as depicted in Figure 8).”

May combine two claims.

In the sense of size parity (and in the sense of population dispersion), polarization regarding women's rights has significantly decreased; society has both moved to greater equality and become more unified (less polarized) on this position.

“In this sense (and in the sense of population dispersion) the polarization regarding women's rights has significantly decreased-society has both moved to greater equality and become more unified (less polarized) on this position.”

May combine two claims.

The increase in party-line voting does not imply that the two parties overlap less on the issue space or that they are moving further apart, but it does imply that individuals within the groups are moving closer to the center of their respective groups.

“That fact itself does not imply that the two parties overlap less on the issue space, or that they are moving further apart, but it does imply that individuals within the groups are moving closer to the center of their respective groups.”

Classified as probably not a substantial claim.

Group consensus for polarization can be measured via any of the previously considered measures of population dispersion: aggregated in-group absolute deviations, variances, pairwise distances, or even aggregated group spreads.

“Group consensus for polarization can be measured via any of the previously considered measures of population dispersion: aggregated in-group absolute deviations, variances, pairwise distances, or even aggregated group spreads.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Since some flat areas may be plateaus or outcroppings from a slope, accounting for this detail in identifying only ranges of minima in a simple formula is not possible.

“Since some flat areas may be plateaus or outcroppings from a slope, accounting for this detail in identifying only ranges of minima in a simple formula is not possible.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Measures for polarization on spatial and network data require different formalisms even for the same senses presented here.

“Measures for polarization on spatial and network data require different formalisms even for the same senses presented here.”

May combine two claims.

The ad hoc way of distinguishing groups by center line always picks out the same number of groups, so it is not a measure of fragmentation.

“Furthermore, because this ad hoc way of distinguishing groups is data-specific and userdefined, it always picks out the same number of groups (so it is not a measure of the fragmentation).”

Probably not a substantial claim: may not pass S3 (load-bearing).

In both groups of voters, the constraint is growing faster than in the populace as a whole.

“In both groups of voters, the constraint is growing faster than in the populace as a whole”

• cites Baldassarri & Gelman, 2008 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The group identification methods described above play a role in the measures that follow.

“While the number of groups acts as a distinct sense of polarization, the group identification methods described above also play a role in the measures that follow.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If the groups are exogenously defined, the overlap between groups works as a pairwise comparison.

“If the groups are exogenously defined then the overlap between groups (the number of individuals in group A that match attitude values with individuals in group B) works as a pairwise comparison.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Many network, grid, or spatial scenarios allow for degrees of group membership resulting in noninteger numbers of groups and partial group membership.

“Furthermore, many of these scenarios allow for degrees of group membership resulting in noninteger numbers of groups and partial group membership.”

May combine two claims.

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

That and other versions are explicitly temporal measures with more restrictions, but they are conceptually the same.

“That and other versions are explicitly temporal measures with more restrictions, but they are conceptually the same.”

Probably not a substantial claim: may not pass S4 (based).

For endogenously defined groups, the number of group boundaries is G-1, so we normalize by dividing by this number to take out the effect of a greater number of groups.

“For endogenously defined groups, the number of group boundaries is G-1, so we normalize by dividing by this number to take out the effect of a greater number of groups.”

Probably not a substantial claim: may not pass S4 (based).

When there are more than two groups in the analysis, some aggregation of the pairwise comparisons must be made that also keeps the measure insensitive to the number of groups and the group size disparities.

“When there are more than two groups in the analysis, some aggregation of the pairwise comparisons must be made that also keeps the measure insensitive to the number of groups and the group size disparities.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Exogenously defined groups provide a way to include categorical data into the analysis framework as long as it is paired with at least one property that holds ordered values along a spectrum.

“Exogenously defined groups provide a way to include categorical data into our analysis framework as long as it is paired with at least one property that holds ordered values along a spectrum.”

Classified as probably not a substantial claim.

Baldassarri and Gelman further note increased consensus among voters in terms of particular issue domains.

“Baldassarri and Gelman further note increased consensus among voters in terms of particular issue domains.”

• cites Baldassarri & Gelman, 2008 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Other researches have examined the interaction terms of the group means and the year.

“Other researches have examined the interaction terms of the group means and the year (Page &, Shapiro 1992).”

• cites Page &, Shapiro 1992Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The relationship between group consensus and polarization holds whether it is the same set of attitudes for both groups or for other areas along the spectrum.

“This holds whether it is the same set of attitudes for both groups or for other areas along the spectrum.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

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

“In applications to higher-dimensional data, endogenously defining the groups requires finding the manifolds of the distributiona well-defined, but much more complicated, similar procedure.”

Classified as probably not a substantial claim.

Baldassarri and Gelman found clear evidence of increasing constraint within issue domains among Republican and Democratic voters, especially among Republicans.

“Looking separately at trends among Republican and Democratic voters we find clear evidence of increasing constraint within issue domains, especially among Republicans.”

• cites Baldassarri & Gelman, 2008 sourceNot checked — no full text of the source

Classified as probably not a substantial claim. May combine two claims.

Our measure tracks the aggregate distances among group means at each time slice, which can then be compared across variables or time.

“Our measure tracks the aggregate distances among group means at each time slice, which can then be compared across variables or time.”

May combine two claims.

Separate groups that are individually more diffuse already admit to a variety of attitudes, so the less consensus held by each group the lower the polarization.

“Separate groups that are individually more diffuse already admit to a variety of attitudes, so the less consensus held by each group the lower the polarization.”

Classified as probably not a substantial claim.

The Kolmogorov-Smirnov two-sample test is a nonparametric way to examine two sets of data and determines the probability that they were drawn from the same distribution, without making any assumptions about what those distributions might be.

“The KS test is a nonparametric way to examine two sets of data and determines the probability that they were drawn from the same distribution, without making any assumptions about what those distributions might be.”

• cites Kaner, Mohanty, & Lyons, 1980 sourceNot checked — no full text of the source
• cites Wilcox, 1997 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

The continuous version of coverage is more valuable when using large datasets for which fine resolution is appropriate and for which the selection of bins biases the results.

“The continuous version is more valuable when using large datasets for which fine resolution is appropriate and for which the selection of bins biases the results.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Democrats have lost constraint on economic and civil rights issues and become a bit more coherent in their moral views.

“In fact, Republicans have become more consistent on economic and civil rights issues, while Democrats have lost constraint on these issues and become a bit more coherent in their moral views.”

• cites Baldassarri & Gelman, 2008 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

The examples above from both DiMaggio et al. and Bartels for distinctness also slide into divergence.

“The examples above from both DiMaggio et al. and Bartels for distinctness also slide into divergence.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

For our current purposes it is sufficient to use the normalized distances among the group means, or the area of the convex hull of the means for more than two groups in more than two dimensions.

“For our current purposes it is sufficient to use the normalized distances among the group means (or the area of the convex hull of the means for more than two groups in more than two dimensions).”

Classified as probably not a substantial claim.

For the community fragmentation sense as a measure of polarization, the number of groups must not be known a priori because that is the feature being measured.

“It is important for this sense as a measure of polarization that the number of groups is not known a priori because that is the feature being measured.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Coverage is valuable for categorical data, especially when data are sparse.

“Though crude, coverage is valuable for categorical data, especially when data are sparse (i.e., the number of observations is small relative to the number of bins/categories).”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

Although there are changes in the number of exogenous groups across time and locations, the endogenous sense is more useful as a measure.

“It is therefore clear that although there are changes in the number of exogenous groups across time and locations, it is the endogenous sense that is more useful as a measure.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The normalized distances among group means measure is applicable whether the groups are defined endogenously or exogenously.

“This measure is applicable whether the groups are defined endogenously or exogenously.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The paper does not take account of response rate variance in its measures.

“We do not take account of this response rate variance in our measures.”

Classified as probably not a substantial claim.

The GSS contains responses to questions on a broad spectrum of topics, including many that are critical for understanding trends in political and social attitudes.

“The GSS contains responses to questions on a broad spectrum of topics, including many that are critical for understanding trends in political and social attitudes.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Neither group consensus nor size parity are explicitly invoked with bimodality.

“Neither group consensus nor size parity are explicitly invoked with bimodality”

May combine two claims.

Although the supposed religious divide exists and is reflected in the groups' political views, it is only slowly widening.

“although the supposed religious divide certainly exists and is reflected in the groups' political views, it is only slowly widening.”

Classified as probably not a substantial claim.

Addressing polarization in a broader topic (such as women's rights, religiosity, or intellectualism) typically requires inferences from examining patterns in multiple questions.

“addressing polarization in a broader topic (such as women's rights, religiosity, or intellectualism) typically requires inferences from examining patterns in multiple questions.”

Classified as probably not a substantial claim.

Esteban and Ray's version of polarization combines at least three senses in the paper's breakdown: there needs to be at least two discernible groups that are both widely divergent and have a strong group consensus.

“This version of polarization combines (at least) three senses in our breakdown: (1) there needs to be at least two discernible groups that are both (2) widely divergent and (3) have a strong group consensus.”

May combine two claims.

Since the lowest value of size parity occurs in 2002, we cannot make the claim that there is an overall increasing trend, only that the sizes of the religiosity groups have been equalizing over the last 10 years of data.

“since the lowest value of size parity occurs in 2002 we cannot make the claim that there is an overall increasing trend, only that the sizes of the religiosity groups have been equalizing over the last 10 years of data.”

Probably not a substantial claim: may not pass S2 (checkable).

Scenarios such as those described obfuscate the varied senses of polarization, thus creating confusion in analyzing polarization patterns.

“We have included this section because we believe that it is scenarios such as these that obfuscate the varied senses of polarization, thus creating confusion in analyzing polarization patterns.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

That widening may be offset by the flattening of political attitudes within the religious groups, and perhaps a disconnecting of religious and political views.

“That widening may be offset by the flattening of political attitudes within the religious groups, and perhaps a disconnecting of religious and political views.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

The paper does not claim that any one of the above senses fully captures any particular widely used notion of polarization, but rather that these senses constitute minimal building blocks of all such notions.

“We do not claim that any one of the above senses fully captures any particular widely used notion of polarization, but rather that these senses constitute minimal building blocks of all such notions.”

May combine two claims.

The increase in polarization in 1996 was not an overall move to the right, but rather a pull in from the right that increased focus on the pure conservative bin.

“The increase in polarization in this case, therefore, is not an overall move to the right, but rather a pull in from the right that increased focus on the pure conservative bin.”

May combine two claims.

In Axelrod's model, the groups are endogenously defined, and the more groups the greater the polarization.

“In this case the groups are endogenously defined, and the more groups the greater the polarization.”

• cites Axelrod, 1997 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

If there is too little consensus or size parity, then the groups may not be visibly discernible as such.

“although if there is too little consensus or size parity then the groups may not be visibly discernible as such.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The effect is amplified among the wealthiest quarter of the population.

“The effect is amplified among the wealthiest quarter of the population.”

• cites Hirschl et al.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable).

Despite their mathematical linkages, the polarization senses detailed here remain conceptually distinct.

“Also keep in mind that despite their mathematical linkages the polarization senses detailed here remain conceptually distinct.”

Classified as probably not a substantial claim.

To measure polarization on the GSS data using the example measures presented above requires limiting application to those topics with appropriate ranked-order scoring systems.

“To measure polarization on the GSS data using the example measures presented above requires us to limit our application to those topics with appropriate ranked-order scoring systems.”

• AssumptionRests on an assumption: The GSS data is representative of the American populace.

Probably not a substantial claim: may not pass S3 (load-bearing).

A further consideration that is left out of the current analysis is the incorporation of confidence into the polarization measures.

“A further consideration that is left out of the current analysis is the incorporation of confidence into the polarization measures.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If the number of groups equals the regionalization plus one, then distinctness is already maximal because the groups have no neighboring or overlapping regions.

“For example, if the number of groups equals the regionalization plus one, then the distinctness is already maximal because the groups have no neighboring or overlapping regions.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The GSS has breadth (> 5,500 variables) and continuity.

“The breadth (> 5,500 variables) and continuity of the GSS makes it an excellent data source for social scientists.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Fiorina and Abrams are invoking distinctness when they measure the drop in moderate view holders.

“Fiorina and Abrams are invoking distinctness when they measure the drop in moderate view holders.”

• cites Fiorina et al., 2010Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable).

Seeing the disparate versions of polarization as different combinations, rather than distinct and incommensurate definitions/measures, ties them together without prioritizing them.

“Seeing them as different combinations, rather than distinct and incommensurate definitions/measures, ties the the disparate versions of polarization together without prioritizing them.”

May combine two claims.

The traits of the agents in Axelrod's model are not cardinal values, and therefore other measures would be required to quantify some aspects of the polarization.

“even though the traits of the agents are not cardinal values and therefore other measures would be required to quantify some aspects of the polarization.”

• cites Axelrod, 1997 sourceNot checked — no full text of the source

May combine two claims.

Axelrod's model also requires group consensus and distinctness of the agents' traits.

“But it also requires group consensus and distinctness of the agents' traits.”

• cites Axelrod, 1997 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable).

These building blocks can be combined in various ways to capture differing, richer notions of polarization while remaining unambiguous about the features of the distribution being described.

“These building blocks can be combined in various ways to capture differing, richer notions of polarization while remaining unambiguous about the features of the distribution being described.”

Classified as probably not a substantial claim.

In Axelrod's model of the dissemination of culture, polarization is characterized by the appearance of regions which are internally homogeneous and have no attributes in common with the other internally homogeneous regions.

“In Axelrod's well-known model of the dissemination of culture, polarization is characterized by the appearance of regions which are internally homogeneous and have no attributes in common with the other internally homogeneous regions (Axelrod, 1997).”

• cites Axelrod, 1997 sourceNot checked — no full text of the source

Classified as probably not a substantial claim. May combine two claims.

The Hirschl et al. analysis reveals that among some Americans (nonsouthern Christian white males) there exists a greater degree of religious belief correlating with a greater likelihood of voting for Republican candidates and a lesser degree of religiosity correlating with a decreasing likelihood of voting Republican.

“The Hirschl et al. analysis reveals (among other things) that among some Americans (nonsouthern Christian white males) there exists a greater degree of religious belief correlating with a greater likelihood of voting for Republican candidates and a lesser degree of religiosity correlating with a decreasing likelihood of voting Republican.”

• cites Hirschl et al.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

Neither divergence nor distinctness is necessary for polarization.

“neither divergence nor distinctness is necessary for polarization”

Classified as probably not a substantial claim.

No single feature of the nine presented here is necessary for polarization.

“no single feature of the nine presented here is necessary”

Probably not a substantial claim: may not pass S2 (checkable).

Polarization is a cluster concept.

“These examples further highlight that polarization is a cluster concept”

Classified as probably not a substantial claim. May combine two claims.

The use of bimodality implies that the population can be most usefully broken down into exactly two subpopulations, and that a balanced deviation from a moderate position is what it means to be polarized.

“The use of bimodality implies that the population can be most usefully broken down into exactly two subpopulations, and that a balanced deviation from a moderate position is what it means to be polarized.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Axelrod's meaning of 'polarization' breaks down into the concepts offered in this paper.

“Axelrod's meaning of 'polarization' nicely breaks down into the concepts offered in this paper”

May combine two claims.

Group consensus is higher because the largest group, Inspired Word, has a lower dispersion than the other two (which are nearly identical), and the group consensus measure averages the three groups without adjusting for their sizes.

“Group consensus is higher because the largest group, Inspired Word, has a lower dispersion than the other two (which are nearly identical), and the group consensus measure averages the three groups without adjusting for their sizes.”

Probably not a substantial claim: may not pass S2 (checkable).

The features of polarization can be combined to form broader definitions as appropriate for the application at hand.

“but the features can be combined to form broader definitions as appropriate for the application at hand.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In calculating the number of endogenously defined groups, a valley with a value of 1.0 between two bins with value 10.0 counts just as much as a valley with a value of 9.9 (although that difference in valley height is picked up with the distinctness measure).

“In calculating the number of endogenously defined groups, for example, a valley with a value of 1.0 between two bins with value 10.0 counts just as much as a valley with a value of 9.9 (although that difference in valley height is picked up with the distinctness measure).”

May combine two claims.

All together the measures indicate that the political polarization of the populace is minor, is confined to specific aspects of the distribution, and is increasing or decreasing depending on the aspect examined.

“All together our measures indicate that the political polarization of the populace (1) is minor, (2) is confined to specific aspects of the distribution, and (3) is increasing or decreasing depending on the aspect examined.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The frequencies of responses in binary or categorical data can reveal trends in attitudes with respect to a specific question.

“Although the frequencies of responses in binary or categorical data can reveal trends in attitudes with respect to a specific question”

May combine two claims.

Because the groups were moving apart, the divergence increased, but because nearly half the respondents are in the middle group, and the groups significantly overlap, the overall population dispersion increases only slightly over the 28-year period.

“Because the groups were moving apart, the divergence increased, but because nearly half the respondents are in the middle group, and the groups significantly overlap, the overall population dispersion increases only slightly over the 28-year period.”

May combine two claims.

None of these polarization measure changes are large because neither public opinion on the topic nor people's religiosity have changed dramatically since 1984.

“None of these polarization measure changes are large because neither public opinion on the topic nor people's religiosity have changed dramatically since 1984.”

May combine two claims.

That is not mathematically implied by the measures, and grouping by a different variable (e.g., ethnicity or education) may reverse one or both of these relationships.

“That is not mathematically implied by the measures, and grouping by a different variable (e.g., ethnicity or education) may reverse one or both of these relationships.”

May combine two claims.

The measures provided operate on a metric space so that there is a clear ordering from one end to the other and distance measures are well-defined everywhere.

“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.”

May combine two claims.

Religiosity explains a small amount of the polarization in people's political views, but it explains a great deal of the polarization in abortion opinions.

“religiosity explains a small amount of the polarization in people's political views, but it explains a great deal of the polarization in abortion opinions.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Count values are weighted using the SDA's composite weight variable.

“Count values are weighted using the SDA's composite weight variable.”

• cites Smith et al., 2013Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

May combine two claims.

American political views tend to be normally distributed, but with fringe groups of varying sizes to both the right and left, while the baseline distribution of abortion opinions is bimodal with varying proportions appearing at the anti-abortion extreme and in the broad valley that separates the two dominant groups.

“American political views tend to be normally distributed, but with fringe groups of varying sizes to both the right and left, while the baseline distribution of abortion opinions is bimodal with varying proportions appearing at the anti-abortion extreme and in the broad valley that separates the two dominant groups.”

• AssumptionRests on an assumption: The GSS samples are representative of the American population, so trends in GSS responses describe Americans' political views and abortion opinions.

May combine two claims.

The more nuanced analysis of the separation of ideas reveals a consistent and persistent division of views on abortion, but not one that is changing coherently over time.

“Our more nuanced analysis of the separation of ideas reveals a consistent and persistent division of views, but not one that is changing coherently over time.”

Classified as probably not a substantial claim. May combine two claims.

The two topics were analyzed both with exogenous groups defined by categories of religiosity, and also filtered by that same variable to ensure the set of respondents was identical.

“These two topics were analyzed both with exogenous groups defined by categories of religiosity, and also filtered by that same variable to ensure the set of respondents was identical.”

• AssumptionRests on an assumption: The BIBLE variable categories (Word of God, Inspired word, Fables) meaningfully capture religiosity differences.

May combine two claims.

For congress voting nominate scores, the mean positions of each party have not significantly moved, but there has been a marked increase in group consensus.

“A similar observation has been made for congress voting nominate scores: the mean positions of each party have not significantly moved, but there has been a marked increase in group consensus (Gelman & Palmer, 2011).”

• cites Gelman & Palmer, 2011Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The largely normal distribution in political views does not breakdown into clear religious groups, but the distribution of abortion opinions does line up.

“Thus the largely normal distribution in political views does not breakdown into clear religious groups, but the distribution of abortion opinions does line up.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

The nine senses presented apply across disciplines and for any property distribution, whether discrete or continuous, although the particular measures used may require adjustment to best handle particular data sets.

“The nine senses presented here apply across disciplines and for any property distribution, whether discrete or continuous, although the particular measures used may require adjustment to best handle particular data sets.”

May combine two claims.

Categorizing by religiosity yields groups that are closer together, more spread out, and share more attitudes than the modes of the data.

“So categorizing by religiosity yields groups that are closer together, more spread out, and share more attitudes than the modes of the data.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The scattered empty bins for the book of fables group in the abortion analysis are likely the result of low sample size in some years.

“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.”

• AssumptionRests on an assumption: The GSS data and SDA composite weights yield valid estimates of Americans' attitudes.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The SDA composite weight adjusts for number of adults in the household, for black oversampling in 1982 and 1987, and for problems with form randomization in 1978-1985, but does not adjust for differential nonresponse.

“This composite weight adjusts for number of adults in the household, for black oversampling in 1982 and 1987, and for problems with form randomization in 1978-1985.It does not adjust for differential nonresponse”

• cites Smith et al., 2013Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The dispersion increase can be attributed entirely to the strongly and moderately religious groups becoming more anti-abortion while not flattening out.

“The dispersion increase can be attributed entirely to the strongly and moderately religious groups becoming more anti-abortion while not flattening out.”

May combine two claims.

When grouped by religiosity, opinions on abortion may be becoming more polarized in the senses that they are getting further apart on average and that the religious group sizes are becoming more similar.

“When grouped by religiosity, opinions on abortion may be becoming more polarized in the senses that they are getting further apart on average and that the religious group sizes are becoming more similar.”

May combine two claims.

With respect to the community fragmentation sense of polarization, political views have recently become nearly as polarized as people's position on abortion, although the distributions look very different.

“With respect to the community fragmentation sense of polarization, political views have recently become nearly as polarized as people's position on abortion, although the distributions look very different.”

May combine two claims.

Existing measures of polarization can be decomposed into our senses, but the translation is not unique.

“Existing measures of polarization can be decomposed into our senses, but the translation is not unique.”