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Political division seems to be one of the main issues of our time, with countless articles, op-eds, and studies describing how the US and other countries (the UK comes immediately to mind) are increasingly divided.

But, aside from perception, how can we know for sure? Are there any ways to measure and quantify political division, ideally in a way that allows comparison between different countries and within a country over time?

  • War is kind of standard, sadly. The stronger or better supported side of the divide wins the war. Also usually gets to set the narrative about who was right and who was wrong. – einpoklum Feb 7 at 6:52
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One way this is measured is public polls. This can be direct public perception polls of another party:

Partisan antipathy rose dramatically compared with 1994, when only 21 percent of Republicans and 17 percent of Democrats had highly unfavorable views of the other. By 2016, those figures had risen to 58 percent and 55 percent, respectively. Even more disturbing, roughly half of voters of each party say the other party makes them feel afraid, while those who say that the policies of the other party are so misguided they are a threat to the nation have risen rapidly. In 2016, 45 percent of Republicans viewed Democratic policies as a threat, up 8 points in just two years; 41 percent of Democrats viewed Republican policies as a threat, up 10 points in two years (Pew Research Center 2016). [1]

Or it might be measured in public perception on partisan issues, such as ability to compromise. For example, the paper [2] talks about a few different things, but it lists several different poll questions asked between 2012 and 2015 showing "Public Opinion Surveys Consistently Show Democrats Are More Amenable to Compromise than Republicans."

One of the more interesting papers I've seen [3] extracts these partisan questions a bit more, and looks at the ability of congress to work together. They are a few different graphs here showing 1) "public laws inacted (figure 6)" has steadily declined since the 80th congress, 2) "Appropriations Bills Passed on Time (figure 7), a bit jumbled chart, but shows the trend is declining since 1977, and 3) "Gridlocked Issues as Proportion of Issues on Agenda (figure 8)" has been trending upward since the 80th congress.

Note: You can probably find some more information exploring related topics. Increased partisan politics is associated with mis-trust of other parties, which leads to

"they are more likely to be willing to accept illiberal measures such as restrictions on freedom of expression or even the use of force against political opponents." [1]

Looking into things like illiberal tendencies, or democratic back sliding (topics covered by the Freedom House surveys) might come up with some additional data.


Sources

[1] United States: Racial Resentment, Negative Partisanship, and Polarization in Trump’s America, Alan Abramowitz and Jennifer McCoy, The ANNALS of the American Academy of Political and Social Science, Vol. 681 Iss. 1, https://doi.org/10.1177/0002716218811309

[2] Compromising Positions: Why Republican Partisans Are More Rigid than Democrats, JAMES M. GLASER and JEFFREY M. BERRY, pp. 99-125 Political Science Quarterly Vol. 133 No. 1 freely available at https://www.psqonline.org/article.cfm?IDArticle=19755

[3] The De-Institutionalization of Congress, ANTHONY J. CHERGOSKY and JASON M. ROBERTS, pp. 475-495, Political Science Quarterly Vol. 133 No. 3 freely available at https://www.psqonline.org/article.cfm?IDArticle=19818

I also left a comment on another post awhile back:

I think polarization is a complex topic. Politically engaged people have moved farther left/right, and assume everyone else has as well, but in reality moderate/centrist/a-political views have remained close to moderate/centrist/a-political (even if the center has shifted). See https://doi.org/10.1146/annurev-polisci-100711-135242 [paywall] and https://doi.org/10.1080/10584609.2015.1038455 [paywall]

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It's a somewhat complex topic (hence the belated answer). Ideological polarization between political parties has been measured for years (in various ways). From a recent paper summarizing the approaches:

Definitions of political polarization usually involve distances in policy stances or attitudes between groups of people, parties, or specific representatives. In his classic study, Giovanni Sartori (1976) identified political polarization as the ideological distance between candidates, parties, and/or voters. [...]

Many studies have relied on weighted variance calculations to devise comparative indices of political party system polarization (PSP; Dalton, 2008; Ezrow, 2007; Hazan, 1995; Pardos-Prado & Dinas, 2010; Taylor & Herman, 1971). A frequently cited formula in recent years was developed by Russell Dalton, using data from the Comparative Study of Electoral Systems, focusing on ideological distances between parties in legislatures as perceived by the public. This formula demonstrates the distance of mean party positions on the Left–Right scale from the mean ideological (Left–Right) position of the legislature as a whole (Dalton, 2008). [...] Ladner (2014) takes this method one step further, measuring spread of party positions in relation to average party system positions, but over multiple issues, and then averaging the scores of all dimensions to produce an index of political system polarization by country-year.

For a more in-depth discussion of measures in the style of Dalton, see Schmitt (2016); there's a giant figure in there giving a visual comparison of the correlations between various indices (all calculated using the same underlying dimensions & data).

These measures generally assume an expert-style rating of parties position on several dimensions. Ladner uses seven dimensions for example: economic liberalization, financial policy [I guess he means fiscal], law and order, immigration policy, environmental protection, welfare state, and finally "liberal society". The ratings can be given by experts or based on public perception. The choice of dimensions too can (of course) produce different results.

Some scholars, for example, have found that voters have difficulty correctly locating parties on issue scales (Carpini & Keeter, 1993; Iyengar, Sood, & Lelkes, 2012). Zechmeister (2015) found that in Latin America, many voters either cannot or will not place themselves on a Left–Right scale [...]

Also, the polarization thus measured between political parties and the public at large has shown little correlation (at least in some studies):

Political elite polarization, however, is not undeniably linked with polarization among the public (Abramowitz, 2010; Fiorina, Abrams, & Pope, 2005). [...] political party polarization measure does not necessarily fully capture polarization at the mass level of society. Pardos-Prado and Dinas (2010), for instance, measured both the party system and mass ideological polarization of European countries by variance of ideological positions, finding the correlation between party system and mass ideological polarization to be relatively weak at r = 0.3.

Another approach to measuring party polarization draws on legislative voting rather than mass public perceptions of party ideological positions. Scholars studying the United States have tended to follow this pattern, creating Dynamic Weighted NOMINAL Three-step Estimation (DW-Nominate; Poole & Rosenthal, 1997) to measure Congressional roll-call votes as indicators of within-party ideological homogeneity and between-party ideological distances. More than two decades of research has shown that the ideological distance between parties in U.S. legislatures at the state and national levels has been growing over time (Davis & Dunaway, 2016; McCarty, Poole, & Rosenthal, 2006; Poole & Rosenthal, 1997; Shor & McCarty, 2011).

The upside of NOMINATE-style methods is that they don't presuppose a number of dimensions (these are extracted from the voting data). The downside is that NOMINATE-style methods are not readily applicable to the general public as there's no meaningful notion of "legislative record" for individuals in the public at large.

As a sort of a compromise, the paper I've been quoting from (Lauka, McCoy and Firat, 2018) proposes a measure of public polarization that

focuses on polarization over parties rather than ideology or any other single political issue [and thus] fits well with the multidimensional nature of political polarization and represents ideological as well as nonideological divisions within societies.

As this is a new method it hasn't been widely used. I see a potentially the issue that the electoral systems of countries, which are generally assumed to affect the number of parties (see Duverger's law) confounding some dimensions. The paper doesn't mention/discuss the issue, as far as I can tell.

As was hinted in the opening quote, another way to look at polarization is the affective dimension. This pretty much treats politics like preferences for (say) football teams, i.e. without trying to get to any ideological roots. At least regarding US politics, this approach has been increasingly popular. See Iyengar et al. (2019) for a recent review. For simpler explanation using "thermometer" style measures, see this Pew report and even maps of that in The Atlantic. As far as I can tell these (affective-focused) methods have not been widely used to study European politics, but there are some recent exceptions with intriguing findings:

The aim of this article is to study the concept of affective polarisation in European party systems. It introduces the Affective Polarisation Index (API) that allows for measuring and comparing levels of affective polarisation also in multiparty systems. This novel measure is applied to 22 European democracies and the United States between 2005 and 2016. The results indicate that affective polarisation is acutely present in European party systems, as partisans are often extremely hostile towards competing parties. The most affectively polarised countries are in Central Eastern and Southern Europe where the degree of affective polarisation is notably higher than it is in the United States, while Northwestern European countries are more moderate in terms of partisan feelings. Further analysis reveals that affective polarisation is significantly correlated with ideological polarisation, but the relationship between the two appears to be conditional: in some Western European political systems ideological polarisation does not lead itself to strong interparty hostility, while in Central Eastern Europe a high degree of affective polarisation can be present even in ideologically centrist party structures. These findings validate the claim that ideological and affective polarisation are two distinct aspects of polarisation, and that the latter also merits additional attention.

Measuring affective polarization in a multi-party (>2) context seems to produce quite different results depending on the metrics used though. Unlike the above (Reiljan, 2019), which used an all-to-all metric, Gidron, Adams, and Horne (2018) using only a left-right metric conclude that even in Western Europe affective polarization is higher than in the US...

in several countries including Spain, France, the UK, and Switzerland, supporters of the largest left- and right-wing parties expressed more intense mutual dislike in every CSES election survey we analyzed than did the American Republican and Democratic supporters in any of the CSES surveys

This is actually somewhat consistent with an empirical observation of Harteveld (2019) that on an all-to-all measure (like Reiljan's) more parties in a country/system correlate with a lower affective polarization. The intuitive explanation of that is that

self-identification with a single party will often be smaller if multiple parties exists that are ideologically close. As a result, a partisan ingroup is not opposed to every possible partisan outgroup to the same extent. A green voter does probably not perceive a typical social democratic voter as a disliked outgroup, or at least not to the same extent as (s)he might consider a conservative voter – let alone a populist radical right voter

Although most affective polarization studies use "thermometer" style scales in their raw data, some have used [trust] game-based measures. One 2018 paper (Westwood et al.) that did that in a cross-country setting found not much difference in four Western countries across party lines, but did find differences across other lines (a nice thing about affective polarization is that it can also be used to compare other divisions in society):

Although in Belgium and Spain measures of divisions due to partisanship overlap those due to social divides, we do not find that partisan animosity is larger in these cases [...]. Also, contrary to expectations, the scope of the partisan divide is similar across the four nations [the other two being US and UK], with all at nearly one unit of currency.

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