1. Duncan MacRae Jr., Issues and Parties in Legislative Voting (Chicago: University of Chicago Press, 1970), 1, 4.

2. The DW-NOMINATE and other ideal point scores are only one facet of the considerable resources compiled and hosted on the www.voteview.com website. Keith Poole and Howard Rosenthal have provided a central and easily accessible site for much of the information on roll call votes and members of Congress compiled by the Inter-university Consortium for Political and Social Research and have undertaken the not inconsiderable task of cleaning up, systematizing, and updating these data. Even without the different measures that they have generated, which are themselves essential for most students of Congress, the site would be an indispensable resource for students of congressional history.

3. Four of these articles had Jeffrey A. Jenkins as first author, suggesting that the range of APD scholars who have found the scores to be useful is even smaller than the count of their use implies. Moreover, several used NOMINATE in only a very limited way, such as using the scores to identify a single member of Congress as liberal or conservative. To be clear, this is not a critique of the authors, who appropriately used the scores to advance their particular research questions. Nor does it mean that these measures are not being used in other sources, such as non-Studies articles and in books. But we suggest the lack of use in the subfield's premier journal is a reflection of the degree to which these scores have been found wanting by many APD scholars interested in Congress. See Jenkins, Jeffrey A., “Partisanship and Confederate Constitution-Making Reconsidered: A Response to Bensel,” Studies in American Political Development 13 (1999): 279–87CrossRefGoogle Scholar; Jenkins, Jeffrey A., “Partisanship and Contested Election Cases in the House of Representatives, 1789–2002,” Studies in American Political Development 18 (2004): 112–35CrossRefGoogle Scholar; Jenkins, Jeffrey A., “Partisanship and Contested Election Cases in the Senate, 1789–2002,” Studies in American Political Development 19 (2005): 53–74 CrossRefGoogle Scholar; Jenkins, Jeffrey A. and Nokken, Timothy P., “Legislative Shirking in the Pre-Twentieth Amendment Era: Presidential Influence, Party Power, and Lame-Duck Sessions of Congress, 1877–1933,” Studies in American Political Development 22 (2008): 111–40CrossRefGoogle Scholar; Lieberman, Robert C., “Weak State, Strong Policy: Paradoxes of Race Policy in the United States, Great Britain, and France,” Studies in American Political Development 16 (2002): 138–61CrossRefGoogle Scholar; Weatherford, M. Stephen, “Presidential Leadership and Ideological Consistency: Were there ‘Two Eisenshowers’ in Economic Policy,” Studies in American Political Development 16 (2002): 111–37CrossRefGoogle Scholar; Schiller, Wendy J., “Building Careers and Courting Constituents: U.S. Senate Representation, 1889–1924,” Studies in American Political Development 20 (2006): 185–97CrossRefGoogle Scholar; Karol, David, “Has Polling Enhanced Representation? Unearthing Evidence from the Literary Digest Issue Polls,” Studies in American Political Development 21 (2007): 16–29 CrossRefGoogle Scholar; Carpenter, Daniel and Sin, Gisela, “Policy Tragedy and the Emergence of Regulation: The Food, Drug, and Cosmetic Act of 1938,” Studies in American Political Development 21 (2007): 149–80CrossRefGoogle Scholar; Valelley, Richard M., “The Reed Rules and Republican Party Building: A New Look,” Studies in American Political Development 23 (2009): 115–42CrossRefGoogle Scholar.

4. Two of the articles using these other roll call–based measures of voting behavior are also by Jenkins, “Partisanship and Contested Election Cases … House,” and “Partisanship and Contested Election Cases … Senate.” The remaining two are James, Scott C., “Building a Democratic Majority: The Progressive Party Mote and the Federal Trade Commission,” Studies in American Political Development 9 (1995): 331–85CrossRefGoogle Scholar; and Farhang, Sean and Katznelson, Ira, “The Southern Imposition: Congress and Labor in the New Deal and Fair Deal,” Studies in American Political Development 19 (2005): 1–30 CrossRefGoogle Scholar.

5. Wawro, Gregory J. and Katznelson, Ira, “Designing Historical Social Scientific Inquiry: How Parameter Heterogeneity Can Bridge the Methodological Divide between Quantitative and Qualitative Approaches,” American Journal of Political Science 58 (2014): 526–46CrossRefGoogle Scholar.

6. See, for example, Caughy, Devin and Schickler, Eric, “Public Opinion, Organized Labor, and the Limits of New Deal Liberalism, 1936–1945,” Studies in American Political Development 25 (2011): 162–89Google Scholar; Sean Farhang, The Litigation State: Public Regulation and Private Lawsuits in the U.S. (Princeton, NJ: Princeton University Press, 2010); White, Steven, “The Heterogeneity of Southern White Distinctiveness,” American Politics Research 45 (2014): 551–78CrossRefGoogle Scholar; Wawro and Katznelson, “Designing Historical Social Scientific Inquiry.”

7. Keith Poole and Howard Rosenthal, Congress: A Political-Economic History of Roll-Call Voting (New York: Oxford University Press, 1997); Keith Poole, Spatial Maps of Parliamentary Voting (Cambridge, UK: Cambridge University Press, 2005).

8. Poole, Keith and Rosenthal, Howard, “D-Nominate after 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll-Call Voting,” Legislative Studies Quarterly 26 (2001), 8 CrossRefGoogle Scholar.

9. Michael Bailey uses explicit position taking by presidents and members of Congress on Supreme Court decisions to estimate a common scale across these institutions. Other important shared reference points are survey responses and campaign contributions. Bailey, Michael A., “Comparable Preference Estimates across Time and Institutions for the Court, Congress, and Presidency,” American Journal of Political Science 51 (2007): 433–48CrossRefGoogle Scholar; Shor, Boris and McCarty, Nolan, “The Ideological Mapping of State Legislatures,” American Political Science Review 105 (2011): 530–51CrossRefGoogle Scholar.

10. Poole and Rosenthal, “D-Nominate after 10 Years,” 8.

11. An additional problem occurs when there are a large number of members whose voting records do not overlap, resulting in missing data in the agreement score matrix used for generating initial estimates of legislator ideal points. Poole developed a linear mapping technique to address this problem, used to create the Common Space scores that allow for comparisons between the House and Senate. Each session and chamber are estimated independently, and member coordinates are regressed against each other, generating predicted coordinates for the bridge members and session and/or chamber-specific linear transformations that can then be applied to those members who served in fewer than five sessions across chambers. Each of the bridge members is assigned their predicted coordinate from the regression, whereas nonbridge members are given the mean of their session-specific adjustments. A single Common Space score is estimated for the entirety of a legislator's tenure. The model as outlined by Poole is $X_0^k = \left[ {{\Psi_k} W_{k}^{\prime} + {J_n} \mu_{k}^{\prime}} \right]_0 + E_0^k $ , where $X_0^k $ is an n by T matrix of legislators, Ψ _k is an n by 1 matrix of legislators coordinates on the k dimension, μ _k is a vector of constants of length T, and $E_0^k $ is an n by T matrix of error terms. The transformation of ideal points for members who do not serve in five chambers is $\hat \Psi _{ik} = \displaystyle{{\mathop \sum \nolimits_{t = 1}^{T_i} \displaystyle{{X_{ikt} - {\hat \mu} _k} \over {{\hat w}_k}}} \over {T_i}}$ , where T _i is the number of sessions in which legislator i served, X _ikt is the ideal point for legislator i in session t on dimension k as generated by the independent scaling, $\hat \mu _k$ is the estimated constant and $\hat w_k$ the estimated coefficient. Note that this is largely the same as the Groseclose, Levitt, and Snyder technique outlined in their article, except that it computes the mean across the session-specific transformations and imputes as a constant ideal point for all members, and that the regression coefficients are not estimated at the session level. Poole, Spatial Maps, 137–39; Groseclose, Tim, Levitt, Steven, and Snyder, James Jr. “Comparing Interest Group Scores across Time and Chambers: Adjusted ADA Scores for the U.S. Congress,” American Political Science Review 93 (1999): 33–50 CrossRefGoogle Scholar.

12. See, for example, James M. Glaser, Race, Campaign Politics, and the Realignment in the South. (New Haven, CT: Yale University Press, 1997).

13. Poole and Rosenthal, “D-Nominate after 10 Years,” 8; Rogers M. Smith, Civic Ideals: Conflicting Visions of Citizenship in U.S. History (New Haven, CT: Yale University Press, 1997); John Gerring, Party Ideologies in America, 1828–1996 (Cambridge, UK: Cambridge University Press, 1998).

14. Member preferences are assumed to be single-peaked and symmetric: That is, as policy moves away from the point of highest preference—the ideal point—they will be worse off, and they will be indifferent between two options that are equally distant from their ideal. Members are presumed to vote sincerely, or if they do vote strategically, then they are assumed do so in a way that preserves the dimensional ordering. If a subset of a legislature is more likely to engage in strategic voting, while other members vote sincerely, then the placement of these members on the recovered dimension will likely be inaccurate. See Poole and Rosenthal, Congress, 17, 147; Rosenthal, Howard and Voeten, Erik, “Analyzing Roll Calls with Perfect Spatial Voting: France 1946–1958,” American Journal of Political Science 48 (2004): 620–32CrossRefGoogle Scholar; Spirling, Arthur and McLean, Iain, “UK OC OK? Interpreting Optimal Classification Scores in the U.K. House of Commons,” Political Analysis 15 (2007): 85–96 CrossRefGoogle Scholar.

15. Poole and Rosenthal, Congress, 4.

16. Since the foundational work in this area, the first dimension has also been interpreted as “partisanship” and the second dimension as “ideology.” Technically, given their definition of ideology (discussed below), both the first and second dimension should be considered “ideology,” but this term is usually reserved for the first dimension. Most discussions of DW-NOMINATE, including the work of Poole and Rosenthal and their coauthors, interpret the first dimension as an ideological dimension related to, but separate, from party. For example, Cheryl Schonhardt-Bailey notes that “the first dimension reflects a liberal-conservative divide over the role of the government in the economy” and that “it is this first dimension that Poole and Rosenthal summarize as ‘ideology.’” McCarty, Poole, and Rosenthal describe the first dimension as “correspond[ing] to the popular conception of liberals versus conservatives.” Cheryl Schonhardt-Bailey, From the Corn Laws to Free Trade: Interests, Ideas, and Institutions in Historical Perspective (Cambridge, MA: MIT Press, 2006), 359, note 6; Nolan McCarty, Keith Poole, and Howard Rosenthal, Polarized America: The Dance of Ideology and Unequal Riches (Cambridge, MA: MIT Press, 2006), 26.

17. Poole and Rosenthal, Congress, 6, 35. As they write on the www.voteview.com site, “The primary dimension is the basic issue of the role of the government in the economy, in modern terms liberal-moderate-conservative” (http://voteview.com/political_polarization2015.html).

18. Poole and Rosenthal, Congress, 51.

19. Ibid., 48; McCarty et al., Polarized America, 50.

20. Poole and Rosenthal, Congress, 46. The second dimension's capturing party loyalty is claimed to be partly responsible for the finding that “a slightly better accounting of roll call votes is gained by using two dimensions, even in periods when the race issue is largely inactive” (Poole and Rosenthal, Congress, 5–6).

21. Philip Converse, “The Nature of Belief Systems in Mass Publics,” in Ideology and Discontent, ed. David Apter (New York: The Free Press, 1964), 207; Gerring, John, “Ideology: A Definitional Analysis,” Political Research Quarterly 50 (1997): 957–94CrossRefGoogle Scholar, 980; Gerring, Party Ideologies in America; Sam DeCanio, Democracy and the Origins of the American Regulatory State (New Haven, CT: Yale University Press, 2015), 35.

22. The idea of a constraint is of central importance to understanding ideology in public opinion research, but here too it remains closely tied to substantive issue positions. Converse, for example, defines “mass belief systems” in terms of a constraint, but the substance of the “specific belief elements” remains the key indicator of liberalism or conservatism. In recapitulating Converse's definition, John Zaller notes that “people who are liberal (or conservative) on one issue tend to be relatively liberal (or conservative) on a range of other issues.” The conservation and liberal issue positions are affixed separately from the fact that they cluster together. In fact, the definition of ideology offered in Congress is perhaps best seen as an instance of an operationalization of a concept for a particular domain—public opinion research—becoming the definition of the concept. Poole, Keith, “Changing Minds? Not in Congress!” Public Choice 131 (2007): 435–36CrossRefGoogle Scholar; Poole and Rosenthal, Congress, 4. See also Noel, Hans, “The Coalition Merchants: The Ideological Roots of the Civil Rights Realignment,” The Journal of Politics 74(2012): 156–73CrossRefGoogle Scholar; Converse, “Nature of Belief Systems,” 208, 209; John Zaller, The Nature and Origins of Mass Opinion (Cambridge, UK: Cambridge University Press, 1992), 113.

23. “The simple ideological structure does not lead to a predictive model for specific issues. True, in the short term one can predict with accuracy…. But to obtain medium- and long-term forecasts, one would need to model how issues map onto the structure” (Poole and Rosenthal, Congress, 5). Although it is not always clear that it is “ideology” that is being measured, for short periods or for a single Congress it is not difficult to leverage other sources of information to discern what perhaps is being reflected in the first and second dimension scores. But to do this systematically across history is a much more difficult undertaking. More importantly, while labeling the dimensional structure “ideology,” arrayed from “liberalism” to “conservatism,” might make sense in some periods, it will be highly anachronistic and misleading in others.

24. “Address of Mr. Stephens, of Mississippi,” Samuel A. Witherspoon, Late a Representative from Mississippi, Memorial Addresses, delivered in the House of Representatives and the Senate of the United States (Washington, DC: Joint Committee on Printing), 74.

25. Rather, the content of the Democratic Party's policy commitments changed dramatically over the twentieth century. This does not mean ideal point estimates and their cross-time comparisons are meaningless. Witherspoon was on the radical side of the Democratic Party, as it was constituted at the time and relative to the Republican opposition. “Address of Mr. Smith, of South Carolina,” Samuel A. Witherspoon, Late a Representative from Mississippi, Memorial Addresses, delivered in the House of Representatives and the Senate of the United States (Washington, DC: Joint Committee on Printing),106; Gerring, Party Ideologies in America.

26. Indeed as Karol notes, opposition to trade liberalization was a position associated with conservatives in the 1950s, but had become a position associated with liberals by the 1980s. David Karol, Party Position Change in American Politics: Coalition Management (Cambridge, UK: Cambridge University Press, 2009), 44. Clarence E. Wunderlin, Robert A. Taft: Ideas, Tradition, and Party in U.S. Foreign Policy (Oxford: Rowman & Littlefield, 2005), 38.

27. Content is generally ascribed by seeing what issue areas seem to be more strongly associated with a given dimension at a given time. More precisely, the proportional reduction in error (PRE) achieved by a one- versus a two-dimensional model is calculated for each vote, and the issue topics for which the PRE increased by 0.2 from adding a second dimension are noted. The “substance” of the second dimension is whatever set of issues most commonly increased the PRE by the requisite threshold during periods in which the increase in the aggregate PRE was most substantial. The aggregate proportional reduction in error is frequently used in analyses of ideal point measures for assessing the improvement in fitting the data by different specifications of a model relative to some benchmark. The benchmark model used in these discussions is the minority vote. A unique PRE is calculated for each vote, and these are aggregated by summing across all votes. $APRE = \displaystyle{{\mathop \sum \nolimits_{j = 1}^n {\left( {Minority\; Vote - Classification\; Errors} \right)}_j} \over {\mathop \sum \nolimits_{j = 1}^n Minority\; Vote_j}}$ . Poole and Rosenthal, Congress, 30.

28. From 1865 until the election of 1896 (the 55th Congress), the second dimension is treated as capturing conflict over bimetallism and the currency. From the turn of the century to the 1940s, there is no consistent pattern, and it becomes a “civil rights” dimension only in the postwar period, and only really for the Senate. See Table 3.2 of Congress for the content of the second dimension in the House. Whereas civil rights does meet the threshold set by Poole and Rosenthal, it does so only in the 89th House. In the Senate, civil rights meets the threshold for most Congresses from the 81st on. More generally, for any estimated dimension, the appropriate interpretation will vary according to specific institutional features and the political context. Parliamentary legislatures, for example, consistently show voting organized along a government-opposition axis, in which the opposition votes en bloc against government proposals even when these move policies toward their preferred outcome. In these contexts, the second dimension can often be interpreted as capturing whatever left or right division is not covered by the government or opposition distinction. But not always, and in many contexts, the second dimension might be a geographical, linguistic, religious, or racial divide, and the left and right divide will not be directly captured at all. See Poole and Rosenthal, Congress, 48–51; Dewan, Torun and Spirling, Arthur, “Strategic Opposition and Government Cohesion in Westminster Democracies,” American Political Science Review 105 (2011): 337–58CrossRefGoogle Scholar; Simon Hix and Abdul Noury, “Government-Opposition of Left-Right? The Institutional Determinants of Voting in Legislatures” (paper presented at the annual meeting of the American Political Science Association, Chicago, 2013); Godbout, Jean-François and Hoyland, Bjorn, “Legislative Voting in the Canadian Parliament,” Canadian Journal of Political Science 44 (2011): 367–88CrossRefGoogle Scholar.

29. One possible response would be that these scores always need to be mapped into two-dimensional space. We agree, although we note that this is not usually done and applies equally to the first as to the second dimension. Nor does it result in scores that are more readily interpretable. For the relative timing of the non-Southern Democratic Party's move to the left of the Republicans on civil rights, see Feinstein, Brian D. and Schickler, Eric, “Platforms and Partners: The Civil Rights Realignment Reconsidered,” Studies in American Political Development 22 (2008): 1–31 CrossRefGoogle Scholar; Jenkins, Jeffery A., Peck, Justin, and Weaver, Vesla M., “Between Reconstructions: Congressional Action on Civil Rights, 1891–1940,” Studies in American Political Development 24 (2010): 57–89 CrossRefGoogle Scholar.

30. It is Poole and Rosenthal, after all, who provide the many labels for the second dimension, precisely because they are sensitive to the fact that the issue content of this dimension, in particular, is unstable.

31. Elizabeth Sanders’ Roots of Reform, for example, identifies a set of agrarian lawmakers who persistently advocated for progressive reforms in Congress, but who repeatedly were forced to make concessions to a pivotal bloc of lawmakers, generally from the Midwest, who were willing to accept the administrative discretion supported by northeastern conservatives.

32. The different techniques rely on different assumptions about the shape of members’ utility curves and about the distribution of error. The differences are not consequential when the policy alternatives lie in the neighborhood of the legislator's ideal point, but they do differ when these alternatives are located far from the legislator's preferred location. As this is more common for extremists, the differences in the utility functions are most consequential at the extremes. The roll call parameters generated by NOMINATE are the midpoints for each dimension as well as the spread, the distance between the location of a yea vote versus a nay vote divided by 2. The status quo and proposal locations can be calculated from the midpoint and spread, but Poole and Rosenthal stress that these values (unlike the midpoint) are poorly estimated. Poole and Rosenthal, Congress, 235; David A. Armstrong, II, Ryan Bakker, Royce Carroll, Christopher Hare, Keith T. Poole, and Howard Rosenthal, Analyzing Spatial Models of Choice and Judgment with R (Boca Raton, FL: CRC Press, 2014), 223–24; Clinton, Joshua, Jackman, Simon, and Rivers, Douglas, “The Statistical Analysis of Roll Call Data,” American Political Review 98 (2004): 356 Google Scholar; See Carroll, Royce, Lewis, Jeffrey B., Lo, James, Poole, Keith T., and Rosenthal, Howard, “The Structure of Utility in Spatial Models of Voting,” American Journal of Political Science 57 (2013): 1011 Google Scholar; Poole, Keith, “A Non-Parametric Unfolding of Binary Choice Data,” Political Analysis 8 (2000): 211–37CrossRefGoogle Scholar.

33. Lee, Frances E., “Agreeing to Disagree: Agenda Control and Senate Partisanship, 1981–2004,” Legislative Studies Quarterly 33 (2011): 199–222 CrossRefGoogle Scholar; Carrubba, Clifford, Gabel, Matthew, and Hug, Simon, “Legislative Voting Behavior, Seen and Unseen: A Theory of Roll-call Vote Selection,” Legislative Studies Quarterly 33 (2008): 543–72CrossRefGoogle Scholar. The logic of the recovered ideal points being sensitive to the location of the cutlines is effectively the same as that laid out in Krehbiel, Keith, “Party Discipline and Measures of Partisanship,” American Journal of Political Science 44 (2000): 212–27CrossRefGoogle Scholar. Although ideal points are an improvement over these other scores, in that they estimate the location of the cutlines, without integrating policy substance, there is no way to know whether the cutlines are comparable over time.

34. Realignment interpretations, for example, argue that extended stretches of American history are characterized by the relative ascendancy of a particular party, ideology, and set of issue priorities. Both the issues under consideration and the political implications of the roll calls being voted on are likely to change considerably across different periods in American history. Because the underlying roll call matrix does not have any information about the location of the policy being considered, but only observed decisions on discrete votes, changes in the process by which roll calls are generated or in the likelihood of voting error can lead to substantial changes in the estimated ideal points. And there is good reason to believe that with differences in agenda control, both across time and institutions, that there will be periods that differ starkly in the mix of roll calls that come to the floor. Roberts, Jason and Smith, Steven, “Procedural Contexts, Party Strategy, and Conditional Party Voting in the U.S. House of Representatives, 1971–2000,” American Journal of Political Science 47 (2003): 305–17CrossRefGoogle Scholar; Clinton, Joshua D. and Lapinski, John, “Laws and Roll Calls in the U.S. Congress, 1891–1994,” Legislative Studies Quarterly 33 (2008): 511–41CrossRefGoogle Scholar.

35. In a similar vein, most existing techniques treat all roll calls as occurring simultaneously, and within a legislative session, the ordering of roll calls can be rearranged without any change in the estimates.

36. The main exception to the practice of constraining individual members’ movements are the one-Congress-at-a-time NOMINATE scores. These are generated by first estimating ideal points and cutlines in the constant model—with no linear change—and then by re-estimating Congress-specific ideal points while holding the roll call parameters fixed. These estimates are rarely used, although we believe they merit greater attention. The DW-NOMINATE framework itself allows for nonlinear scores: Legislators’ scores across time are modeled as a polynomial function of time, so that legislator i's ideal point on dimension k at time t is X _ikt  = γ _ik0 + γ _ik1 T _t1 + γ _ik2 T _t2 + … + γ _ikv T _tv , where v is the degree of the polynomial, γ are the coefficients of the polynomial, and the Ts are Legendre polynomials. For DW-NOMINATE, v is set at 1—estimating a linear score—because Poole and Rosenthal found that “essentially all movement is captured by simple linear movement,” and that “the linear model in two dimensions was the best combination of explanatory power and number of parameters.” The modeling decisions made by Poole and Rosenthal were carefully thought through and have been persuasively defended as justified relative to the potential gains of a parsimonious measure that can be compared across the entirety of American history. Poole, Spatial Models, 104–107; Poole and Rosenthal, Congress, 25, 236; Nokken, Timothy and Poole, Keith, “Congressional Party Defection in American History,” Legislative Studies Quarterly 29 (2004): 545–68CrossRefGoogle Scholar.

37. Groseclose et al., “Comparing Interest Group Scores.”

38. Specifically, the method estimates a latent dimension, y _it  = α _t  + β _t x _i  + ε _it , with x _i being a mean-preference parameter—initially the mean score for a member over that member's entire career—and ε _it being an error term capturing individual change.

39. Given that these two measures are highly correlated in one dimension, the following discussion focuses on W-NOMINATE. The scores discussed in Sections 3.2 and 3.3, by contrast, were estimated with IDEAL. As with the Common Space scores, GLS-adjustments relies on bridge actors who served in both the House and the Senate, with the distinct advantage that rather than a static ideal point, members have scores that reflect the independently estimated sessions that are being adjusted.

40. Barry Burden, for example, demonstrates that individual events in legislators’ lives can dramatically alter their preferences. Barry Burden, Personal Roots of Representation (Princeton, NJ: Princeton University Press, 2007).

41. David Binder, “Jamie Whitten, Who Served 53 Years in House, Dies at 85,” New York Times, Sept. 10, 1995, http://www.nytimes.com/1995/09/10/obituaries/jamie-whitten-who-served-53-years-in-house-dies-at-85.html.

42. Katznelson, Ira and Mulroy, Quinn, “Was the South Pivotal? Situated Partisanship and Policy Coalitions during the New Deal and Fair Deal,” Journal of Politics 74 (2012): 604–20CrossRefGoogle Scholar.

43. The assumption that the mean ideal point of members who continuously serve together without any turnover remains stable is an extension of work on judicial ideology. Baum, Lawrence, “Measuring Policy Change in the U.S. Supreme Court,” American Political Science Review 82 (1988): 905–12CrossRefGoogle Scholar; Groseclose et al., “Comparing Interest Group Scores,” 36.

44. That is, if sitting members on average drifted to the left during this period, then the recovered space would be presumed to be more conservative than it actually was. This is a fundamental problem with all scaling methods, none of which can fully account for changes in the underlying space. This is one of the central motivations for integrating information about the policy agenda into the ideal point estimates themselves. Another limitation to linear mapping methods such as GLS is that the different chambers or sessions being adjusted must be on the same underlying dimension. This is often relatively straightforward, but when it is not the case, the procedure will in effect be regressing two different sets of coordinates. In the case of GLS, the regression coefficient will accordingly be small. Recall that the regression coefficient β is used as the stretch parameter and the denominator in the adjustment formula $\hat y_{it} = \displaystyle{{y_{it} - \alpha _t} \over {\beta _t}}$ . As β decreases in size, $\hat y_{it}$ will increase, and the adjustment will lead to exploding estimates.

45. See Hans Noel, “Separating Ideology from Party in Roll Call Data: Why NOMINATE Doesn't Measure Ideology but Can Be Used to Measure Polarization,” and Devin Caughy and Eric Schickler, “Structure and Change in Congressional Ideology: NOMINATE and Its Alternatives” (papers presented at the Congress & History Conference, University of Maryland, College Park, June 11–12, 2014).

46. As we have seen, the way in which issue substance is usually handled in an ideal point context is to treat the dimensions as recovering distinct positions across different issues. Although most early research on roll call voting in Congress had concluded that members “respond to many issues in terms of fairly broad evaluative dimensions,” Poole and Rosenthal's work drastically reduced the number of dimensions from four or five to at most two, with the first dimension doing most of the work and the second at best a “second fiddle.” Miller, Warren and Stokes, Donald, “Constituency Influence in Congress,” American Political Science Review 57 (1963): 45–56 CrossRefGoogle Scholar, 47; Poole and Rosenthal, Congress, 54; Poole, Keith and Rosenthal, Howard, “Dimensional Simplification and Economic Theories of Legislative Behavior,” Economics and Politics 6 (1994):163–71CrossRefGoogle Scholar, 171.

47. The question of over what votes to aggregate—by issue area, by type of vote, by legislative period—is shared across all analyses of roll call data, including those that calculate party unity or Rice cohesion scores. See V. O. Key, Southern Politics in State and Nation (New York: Alfred A. Knopf, 1949); Duncan MacRae Jr., Parliament, Parties, and Society in France, 1946–1958 (New York: St. Martin's Press, 1967); Aydelotte, William O., “Voting Patterns in the British House of Commons in the 1840s,” Comparative Studies in Society and History 5 (1963): 134–63CrossRefGoogle Scholar; Crespin, Michael H. and Rohde, David W., “Dimensions, Issues, and Bills: Appropriations Voting on the House Floor,” The Journal of Politics 72 (2010): 976–89CrossRefGoogle Scholar; and John Lapinski, The Substance of Representation: Congress, American Political Development, and Lawmaking (Princeton, NJ: Princeton University Press, 2013).

48. The main advantage of this issue scheme in particular is that it is nested, with each roll call assigned a code corresponding to a set of fine-grained and deductively generated issue categories, which are then aggregated into bulkier categories corresponding to issue areas common to most sovereign states and national legislatures. The virtue of this arrangement for estimating ideal points is that it helps overcome the problem of insufficient data. There are unlikely to be sufficient roll calls on the question of “religion” in many Congresses to reliably estimate a set of issue-specific scores. But at the cost of some precision, we can treat the question of “religion” as bound up with other questions with which it is closely related, such as “loyalty and expression” or “privacy.” We can then estimate scores for a bulkier category that theoretically encompasses the more fine-grained issue codes. Ira Katznelson and John S. Lapinski, “The Substance of Representation: Studying Policy Content and Legislative Behavior,” in The Macropolitics of Congress, ed. E. Scott Adler and John S. Lapinski (Princeton, NJ: Princeton University Press, 2006), 96–126.

49. In Congress, Poole and Rosenthal estimated ideal points for five distinct issue areas in the 95th House of Representatives, finding that the ideal points had high correlations across issue areas. Poole and Rosenthal, Congress, 55.

50. These are equivalent to the GLS-adjusted W-NOMINATE scores in Section 3.1.

51. See Richard L. Wilson, “Fulbright, J. William,” in American Political Leaders, American Biographies (New York: Facts On File, 2002).

52. Eileen Boris, “‘No Right to Layettes or Nursing Time’: Maternity Leave and the Question of U.S. Exceptionalism,” Workers across the Americas: The Transnational Turn in Labor History, ed. Leon Fink (Oxford: Oxford University Press, 2011), 171–93, 185; Eileen Boris, “Sen. William Langer,” The Afro-American, Nov. 21, 1959.

53. For example, if each party caucus was divided evenly into three blocs—liberals, moderates, and conservatives—nearly 20 percent of House members would at some point be characterized as “liberal” and “conservative” across these two issue areas.

54. We follow Clinton and colleagues in identifying likely pivotal members by (1) sampling legislators’ ideal points from the joint posterior distribution, (2) ranking the sampled ideal points, (3) identifying which member is in the pivotal position, and (4) repeating this a large number of times, reporting the proportion of times that a set of legislators are in the relevant position. See Clinton et al., “Statistical Analysis of Roll Call Data,” 360. The dashed line is the mean proportion for those members who were at any point identified as the median member.

55. Note that the median pivot is more precisely estimated than the surrounding members.

56. In other work we have estimated two sets of pooled ideal points in the area of labor policy, but pooled only those Congresses before and after a suspected inflection point so as to not include information from after the inflection in the first set of estimates. Bateman, David, Katznelson, Ira, and Lapinski, John, “ Southern Politics Revisited: On V. O. Key's ‘South in the House,’” Studies in American Political Development 29 (2015): 154–84CrossRefGoogle Scholar.

57. Incorporating substantive information can both increase our understanding of policy change while mitigating to a certain extent the problem of sparse data. For example, we might have very strong priors about certain members, or we might have alternative but incomplete measures of policy liberalism. By integrating these into the estimates, we are able to use fewer roll calls more efficiently.

58. Bonica, Adam, “Punctuated Origins of Senate Polarization,” Legislative Studies Quarterly 39 (2014): 5–26 CrossRefGoogle Scholar.

59. For more information on this procedure, see Bateman et al., “Southern Politics Revisited.”

60. The quick reversal of positions suggests that this particular twenty-week period might be on a different dimension than the others, making the use of GLS problematic. Where this occurs, it might make sense for the researcher to drop those periods that are off-dimension. But this technique also allows the researcher to note when such off-dimensional debates punctuate congressional voting, rather than reducing these to a single second-dimensional score estimated for the entire Congress.

61. Londregan, “Estimating Legislators’ Preferred Points,” Political Analysis 8, no. 1 (1999): 36 Google Scholar.

62. We only include votes on the Social Security program, rather than Medicare or other programs attached to the Social Security Act.

63. The midpoint is halfway between the existing status quo and the new proposal. If this proposal passes, as the five identified roll calls did, then the location of the policy proposal becomes the new status quo point. If a subsequent proposal would liberalize the program further, then the new roll call midpoint should be located to the left of the previous roll call midpoint.

64. In imputing votes based on inferred policy positions, we are following Bailey, “Comparable Preference Estimates.” For our purposes, imputing votes and constraining the midpoints are effectively equivalent, and we rely on the former approach here.

65. Shor, Boris, Berry, Christopher, and McCarty, Nolan, “A Bridge to Somewhere: Mapping State and Congressional Ideology on a Cross-Institutional Common Space,” Legislative Studies Quarterly 35 (2010): 417–48CrossRefGoogle Scholar.

66. Many Republicans did support moving the program more fully to a pay-as-you-go system funded through income taxes, but this was the extent of opposition, and the Senate passed the bill 81–2 and the House passed the conference report by 374–1. Even the lone Republican who voted nay explained that he felt obliged to vote against, as he had offered a motion to recommit as a tactical measure intended to save an amendment concerning when the federal government could withhold compensation funds from the states, and under House rules only those opposed to the bill could propose recommittal. “Social Security Act,” in CQ Almanac 1950, 6th ed., (Washington, DC: Congressional Quarterly, 1951), 165–77. http://library.cqpress.com/cqalmanac/cqal50-1377221.

67. Joshua Clinton and Adam Meirowitz also generate nonagnostic scores that integrate information about the roll call parameters. They note that given the underlying behavioral model the ordering of votes in a given session should matter, but that under standard techniques it does not. The status quo point changes with each roll call, but this fact is disregarded in most estimation techniques because we do not have an independent ability to locate the status quo or the proposal in a common space. They propose a model in which the estimated location of the winning position of the immediately preceding roll call is used as the status quo point for the next roll call to occur in the same issue area. See Clinton, Joshua D. and Meirowitz, Adam, “Testing Explanations of Strategic Voting: A Reexamination of the Compromise of 1790,” American Journal of Political Science 48 (2004): 675–89CrossRefGoogle Scholar; Bailey, “Comparable Preference Estimates,” 442, 439.