1. If one enters “political polarization” into the search field for the Chronicle tool of the New York Times, http://chronicle.nytlabs.com/, one sees that the term takes off immediately after 2006, which coincides with the publication of the landmark study (first published in 2006, now in its second edition) by Nolan McCarty, Keith T. Poole, and Howard Rosenthal, Polarized America: The Dance of Ideology and Unequal Riches (Cambridge, MA: MIT Press, 2016).

2. For an essential review essay, see Marc Hetherington, “Putting Polarization in Perspective,” British Journal of Political Science 39 (Apr. 2009): 413–48.

3. Keith T. Poole and Howard Rosenthal, Congress: A Political-Economic History of Roll Call Voting (New York: Oxford University Press, 1997).

4. Shor extended the basic algorithm to state legislatures, see Boris Shor and Nolan McCarty, “State Legislative Ideology Data,” Measuring American Legislatures, http://americanlegislatures.com/.

5. An early, oft-cited introduction is Jordan Ellenberg, “Growing Apart: The Mathematical Evidence for Congress’ Growing Polarization,” Slate (Dec. 26, 2001), http://www.slate.com/articles/life/do_the_math/2001/12/growing_apart.html. A fine discussion is Nolan McCarty, “Measuring Legislative Preferences,” in Oxford Handbook of the American Congress, ed. George C. Edwards III, Frances E. Lee, and Eric Schickler (New York: Oxford University Press, 2011), 66–94.

6. Nolan McCarty, “Polarization and American Political Development,” in Oxford Handbook of American Political Development, ed. Richard M. Valelly, Suzanne Mettler, and Robert C. Lieberman (New York: Oxford University Press, 2016), 492–515.

7. For a full list see “National Special Interest Groups,” Vote Smart: Just the Facts, https://votesmart.org/interest-groups#.VwGCCRMrK8o.

8. Tim Groseclose, Steve Levitt, and James Snyder, “Comparing Interest Group Scores across Time and Chambers: Adjusted ADA Scores for the U.S. Congress,” American Political Science Review 93 (Mar. 1999): 33–50.

9. Anyone who is aware of the Policy Agendas Project will appreciate such issue variety, see “About the Project,” Policy Agendas Project, http://www.policyagendas.org/page/about-project. For an overview of the Policy Agendas Project, see “Visualizing Policy Agendas,” Texas Liberal Arts, http://www.utexas.edu/cola/laits/features/_features/Visualizing-Policy-Agendas.php.

10. The example of Bayesian approaches to recovering where legislators are in issue space suggests why the scores correlate so strongly. Scores derived from Bayesian approaches depend on “vague priors”; that is, they assume very little about the actual location of legislators, thus approximating the frequentist premise that data are random. So they tend to converge on frequentist results, leading to the high correlations. An accessible introduction to these matters can be found in Joshua Clinton, Simon Jackman, and Douglas Rivers, “The Statistical Analysis of Roll Call Data,” American Political Science Review 98 (May 2004): 355–70.

11. Poole and Rosenthal began their exposition of the algorithm in Congress, 233.

12. Sarah Binder, Thomas Mann, Alan Murphy, and Paul Sahre, “Where Do They Stand?” Op-Chart, New York Times, July 26, 2004, A-17.

13. Note that what follows sounds more like a quadratic utility function, with the two sides of a bell-shaped function crossing the abscissa, but the utility model used by Poole and Rosenthal is meant to take account of legislator awareness of precise ideological differences. Thus the function has two tails that never cross the abscissa. In order to sketch the spatial model, we have ignored this critical difference.

14. We are deliberately vague about the precise number because it turns out that roll call voting is an institution with several dimensions that have changed over time, including its frequency. For a fascinating treatment, see Michael S. Lynch and Anthony J. Madonna, “Viva Voce: Implications from the Disappearing Voice Vote,” Social Science Quarterly 94 (June 2013): 1–21. The complexity and procedural evolution of roll call voting do not, however, affect the scaling that NOMINATE does nor do they affect the finding of “low” dimensionality, that is, that over the course of American political development, congressional roll call voting does not display more than two fundamental issue spaces or dimensions.

15. See the Appendix at the end of this article, the row for DW-NOMINATE (DW stands for “dynamically weighted.”). The substantive point here is that legislator utility functions are modeled as ellipses not circles. For a very clear discussion of the difference and its significance, see Charles Stewart III, Analyzing Congress, 2nd ed. (New York: W.W. Norton, 2011), chap. 1.

16. The authors used a variant called “Common Space” scores; these are not available for the entire period of congressional history.

17. See Hans Noel, Political Ideologies and Political Parties (New York: Cambridge University Press, 2014.) An important illustration is Monica Prasad, “The Popular Origins of Neoliberalism in the Reagan Tax Cut of 1951,” Journal of Policy History 23 (July 2012): 351–83. See also Wesley Hussey and John Zaller, “Who Do Parties Represent?” in Who Gets Represented?, ed. Peter K. Enns and Christopher Wlezien (New York: Russell Sage Foundation, 2011), 311–44. The “it's ideology” view gains considerable support from the work that has gone into creating a very useful complement to NOMINATE scores, namely Crowdpac scores (the brainchild of Stanford's Adam Bonica); see “Crowdfund U.S. Politics: With Crowdpac Campaigns,” Crowdpac, https:// www.crowdpac.com/.

18. See Frances E. Lee, Beyond Ideology: Politics, Principles, and Partisanship in the U.S. Senate (Chicago: University of Chicago Press, 2009.) On the relationship between agenda construction and party polarization, see Laurel Harbridge, Is Bipartisanship Dead? Policy Agreement and Agenda-Setting in the House of Representatives (New York: Cambridge University Press, 2015.) Also, Sean Theriault, “Partisan Warfare is the Problem,” Political Polarization in American Politics, ed. John Sides and Daniel Hopkins (New York: Bloomsbury Academic, 2015), 11–15; and Frances E. Lee, “American Politics Is More Competitive Than Ever, and That Is Making Partisanship Worse,” Political Polarization in American Politics, ed. John Sides and Daniel Hopkins (New York: Bloomsbury Academic, 2015), 76–79. Although not intended as a synthesis of the debate, see Barbara Sinclair, Party Wars: Polarization and the Politics of National Policy Making (Norman: University of Oklahoma Press, 2006.) For an excellent treatment of various models of party politics, see Raymond La Raja and Brian Schaffner, Campaign Finance and Polarization: When Purists Prevail (Ann Arbor: University of Michigan Press, 2015), chap. 1.

19. See, for example, Jacob Jensen, Ethan Kaplan, Suresh Naidu, and Laurence Wilse-Sansom, “Political Polarization and the Dynamics of Political Language: Evidence From 130 Years of Partisan Speech,” Brookings Papers on Economic Activity (Fall 2012): 1–60. For a fascinating example of text-as-data developmental analysis in a different national context, see Arthur Spirling, “Democratization and Linguistic Complexity: The Effect of Franchise Extension on Parliamentary Discourse, 1832–1915,” Journal of Politics 78, no. 1 (Jan. 2016): 120–36.

20. Among others, Ira Katznelson, When Affirmative Action Was White: An Untold History of Racial Inequality in Twentieth-Century America (New York: W.W. Norton, 2005); Robert C. Lieberman, Shifting the Color Line: Race and the American Welfare State (Cambridge, MA: Harvard University Press, 1998); Steve Valocchi, “The Racial Basis of Capitalism and the State, and the Impact of the New Deal on African Americans,” Social Problems 41, no. 3 (Aug. 1994): 347–62.

21. Poole and Rosenthal, Congress, 28, table 3.1.

22. This pattern also extends to other countries’ legislatures. Rosenthal and Voeten found that a two-dimensional model in the French Fourth Republic—a legislature with unstable party memberships and a variety of parties and factions ranging from Socialists and Communists to right-wing parties—can predict 96.2 percent of vote choices correctly, and that adding a third dimension only increases the predictive ability by 0.8 percent. See Howard Rosenthal and Erik Voeten, “Analyzing Roll Calls with Perfect Spatial Voting: France 1946–1958,” American Journal of Political Science 48 (July 2004): 620–32.

23. There are several kinds of scores, but DW-NOMINATE is the one that is most frequently used and the one that allows cross-time comparison. The Appendix at the end of this article lists the various types of scores. For an intuitive discussion of why these scores are dynamically weighted and for why they allow cross-time comparability, see McCarty, “Polarization and American Political Development.”

24. The alert reader will notice that Rankin's second-dimension score is actually just over the upper bound. This might seem the result of truly fierce white supremacism. That is, in fact, the explanation. The technical reason for his score being above the upper limit is related to the estimates of whether his ideal points move in issue space across time. Poole and Rosenthal found that most legislators do move their location in issue space, and they do this somewhat over time. Their movement is best estimated as a linear movement. On the whole, however, movement is slight. See Poole and Rosenthal Congress, 25, 28, 70–77. If, therefore, someone has moved over the bound on any dimension, the score indicates that there were political pressures that moved the legislator a great deal, relative to other legislators. Thus, Rankin's white supremacism caused him to move in issue space quite a bit over the course of his career and relative to all other legislators, which reflects his reaction to the destruction of Jim Crow between the New Deal and the Great Society.

25. DeWitt, Larry, “The Decision to Exclude Agricultural and Domestic Workers from the 1935 Social Security Act,” Social Security Bulletin 70, no. 4 (2010): 49–68 Google Scholar, http://www.ssa.gov/policy/docs/ssb/v70n4/v70n4p49.html.

26. We use the older plots in our discussion because the new website went live just as this article was in production.

27. Note that north–south is nothing more than a pun; Any second dimension vote, for example, on abortion—if the House ever voted a national policy proposal—would be north–south.

28. It is worth noting that one might consider the cutline angles from a broader perspective. A way to measure whether there is particularly notable second-dimension activity in a given Congress is to calculate the proportion of roll calls that have an angle between −45 and 45 degrees—in other words, the proportion of roll calls where the second dimension was more explanatory than the first dimension. Figuring that out can be done by navigating to the Voteview website and accessing the data on angles. Congresses with a relatively high proportion of second-dimension activity could be investigated and contrasted with Congresses that are not second-dimension Congresses.

29. Sean Farhang and Ira Katznelson, “The Southern Imposition: Congress and Labor in the New Deal and Fair Deal,” Studies in American Political Development 19 (Spring 2005): 1–30, note 40. To be clear, Robert Lieberman first argued that Social Security was covertly racialized in Shifting the Color Line: Race and the American Welfare State (Cambridge, MA: Harvard University Press, 2001.)

30. DeWitt, “Decision to Exclude Agricultural and Domestic Workers”; Gareth Davies and Martha Derthick, “Race and Social Welfare Policy: The Social Security Act of 1935,” Political Science Quarterly 112 (Summer 1997): 217–35.

31. A superb overview is Lee, Frances E., “How Party Polarization Affects Governance,” Annual Review of Political Science 18 (2015): 261–82CrossRefGoogle Scholar.

32. Stephen Ansolabehere, Jonathan Rodden, and James M. Snyder Jr., “Purple America,” Journal of Economic Perspectives 20 (Spring 2006): 97–118.

33. One side says the mass-level change is real; see Alan Abramowitz, The Disappearing Center: Engaged Citizens, Polarization, and American Democracy (New Haven, CT: Yale University Press, 2010). See also “Political Polarization in the American Public,” Pew Research Center (June 12, 2014), http://www.people-press.org/2014/06/12/political-polarization-in-the-american-public/; Christopher Hare and Keith T. Poole, “How Politically Moderate Are Americans? Less Than It Seems,” Political Polarization in American Politics, ed. John Sides and Daniel Hopkins (New York: Bloomsbury Academic, 2015), 32–40; and David Broockman, “Are Politicians and Activists Reliably ‘More Extreme’ Than Voters? A Skeptical Perspective,” Political Polarization in American Politics, ed. John Sides and Daniel Hopkins (New York: Bloomsbury Academic, 2015), 47–54. Another side says that the change is an elite phenomenon and a symptom of the political irresponsibility of professional party politicians. A clear statement is Michael W. McConnell, “Moderation and Coherence in American Democracy,” California Law Review (The Brennan Center Jorde Symposium on Constitutional Law) 99 (Apr. 2011): 373–88. The basic statement is Morris P. Fiorina, with Samuel J. Abrams and Jeremy C. Pope, Culture War? The Myth of a Polarized America, 3rd ed. (New York: Longman, 2010.) See also Mark A. Smith, Secular Faith: How Culture Has Trumped Religion in American Politics (Chicago: University of Chicago Press, 2015.) A position that combines elite and mass level analysis and introduces the concept of sorting is Matthew Levendusky, The Partisan Sort: How Liberals Became Democrats and Conservatives Became Republicans (Chicago: University of Chicago Press, 2009). For a similar finding and very helpful conceptual discussion see Delia Baldassarri and Andrew Gelmn, “Partisans Without Constraint: Political Polarization and Trends in American Public Opinion,” American Journal of Sociology 114 (Sept. 2008): 408–46, and see, as well, Joseph Bafumi and Robert Y. Shapiro, “A New Partisan Voter,” Journal of Politics 71 (Jan. 2009): 1–24, showing that voters have become more issue-aware and partisan. A fourth view is that mistrust—not growing ideological incompatibility—is the key mass-level variable: Marc Hetherington and Thomas J. Rudolph, Why Washington Won't Work: Polarization, Political Trust, and the Governing Crisis (Chicago: University of Chicago Press, 2015.)

34. Sarah Binder and Mark Spindel, “Independence and Accountability: Congress and the Fed in a Polarized Era,” Strengthening American Democracy 123 (Washington, DC: The Brookings Institution, Apr. 2016).

35. For the politics of wage theft, see Daniel Galvin, “Deterring Wage Theft: Alt-Labor, State Politics, and the Policy Determinants of Minimum Wage Compliance,” Perspectives on Politics 14, no. 2 (June 2016): 324–50.

36. Christopher Faricy, Welfare for the Wealthy: Parties, Social Spending, and Inequality in the United States (New York: Cambridge University Press, 2015).

37. Sarah Binder, Stalemate: Causes and Consequences of Legislative Gridlock (Washington, DC: The Brookings Institution Press, 2003); Binder, Sarah, “The Dysfunctional Congress,” Annual Review of Political Science 18 (2015): 85–101 CrossRefGoogle Scholar (updating findings from Stalemate); McCarty et al., Polarized America; Nolan McCarty, “The Decline of Regular Order in Congress: Does It Matter?” in Congress and Policy Making in the 21st Century, ed. Jeffery A. Jenkins and Eric M. Patashnik (New York: Cambridge University Press, 2016), 162–86; and, Richard Pildes, “Romanticizing Democracy, Political Fragmentation, and the Decline of American Government,” Yale Law Journal 124 (December 2014): 806–52.

38. For a very important recent discussion, see the essays in Nathaniel Persily, ed., Solutions to Political Polarization in America (New York: Cambridge University Press, 2015); Kelly Williams, “The Brennan Center Jorde Symposium: “Ungovernable America? The Causes and Consequences of Polarized Democracy,” Apr. 22, 2010, http://www.brennancenter.org/blog/ungovernable-america-jorde-symposium. See also Thomas Mann and Norman Ornstein, It's Even Worse Than It Looks: How the American Constitutional System Collided with the New Politics of Extremism, rev. ed. (New York: Basic Books, 2016). For examples of work that finds silver linings in polarization or that caution that the pathology of polarization can be overstated, see Abramowitz, Disappearing Center; Thomas Keck, Judicial Politics in Polarized Times (Chicago: University of Chicago Press, 2014); and Russell Muirhead, The Promise of Party in a Polarized Age (Cambridge, MA: Harvard University Press, 2014).

39. Michael J. Barber and Nolan McCarty, “Causes and Consequences of Polarization,” Solutions to Political Polarization in America, ed. Nathaniel Persily (New York: Cambridge University Press, 2015), 15–58; and Nolan McCarty, “Reducing Polarization by Making Parties Stronger,” Solutions to Political Polarization in America, ed. Nathaniel Persily (New York: Cambridge University Press, 2015), 136–45. Also, the very important study by La Raja and Schaffner, Campaign Finance and Polarization.

40. Jacob Hacker and Paul Pierson, “Confronting Asymmetric Polarization,” in Solutions to Political Polarization in America, ed. Nathaniel Persily (New York: Cambridge University Press, 2015), 59–70.

41. A fine effort along these lines is La Raja and Schaffner, Campaign Finance and Political Polarization.

42. An early effort along these lines is David Brady and Hahrie Han, “Polarization Then and Now: A Historical Perspective,” in Red and Blue Nation? Characteristics and Causes of America's Polarized Politics, vol. 1, ed. David Brady and Pietro Nivola (Washington, DC: The Brookings Institution Press, 2006). See also David Karol, “American Political Parties: Exceptional No More,” in Solutions to Political Polarization in America, ed. Nathaniel Persily (New York: Cambridge University Press, 2015), 208–17.

43. A suggestive work in this connection is Edward Foley, Ballot Battles: The History of Disputed Elections in America (New York: Oxford University Press, 2016).