THE RELATIONSHIP BETWEEN LANGUAGE AND THE NOMINATE ALGORITHM

Let me begin by briefly reviewing what the NOMINATE algorithm actually does. For any set of roll calls in which individuals publicly cast votes, the algorithm processes these votes (the raw data) into numerical coordinates that basically relate each individual's voting record to every other individual's voting record.Footnote ⁴ The resulting numerical coordinates are often (but not always) converted into a two-dimensional display. What the analyst receives, in terms of output from the statistical processing of the data, is thus a two-dimensional display of “dots.” Each of these dots (hereafter referred to as “points”) is a statistical artifact produced by the algorithm by mathematically processing an individual voting record in tandem with other individual voting records.

The algorithm itself tells us nothing about what these points represent with respect to empirical reality. In fact, even when we know that the data that have been processed are composed of roll calls, a point produced by the algorithm cannot be simply traced back to an individual voting record because the calculation of the statistical artifact is dependent upon the other individual voting records included in the data set. That means that the exclusion of some individuals or some votes from the data set will alter the array of points in the two-dimensional display. What the algorithm produces is simply an array of points in a two-dimensional frame that, when first inspected, has no intuitively obvious meaning to the observer.Footnote ⁵

The algorithm will produce numerical coordinates and, thus, two-dimensional displays out of any data that can be translated into binary categories. For example, the binary categories could be whether or not it rained on particular days in a given year, the individuals could be different weather stations in a country, and the data set could be the rainfall record at each of these stations. The NOMINATE algorithm could process this data set into coordinates and displays in the same way that it processes roll call votes, and the analyst, when presented with the statistical artifacts thus produced, would have no way of knowing whether it was votes or rainfall that had been processed. Let us take a moment and allow the implications of these observations sink in. When the observer views the two-dimensional display produced by the algorithm, there is no intuitively obvious meaning arising out of the array of points. The array produced by rainfall patterns will look the same, for all intents and purposes, as that produced by roll call votes. The observer would not be able to distinguish between the two displays simply by viewing them.Footnote ⁶

When someone adopts the social conventions and interpretive norms of the NOMINATE community, they begin to “see” the two-dimensional array in much the same way as someone might “see” a blot in a Rorschach test.Footnote ⁷ And, just as the same Rorschach test cannot be used across different cultures, the interpretation of these two-dimensional displays does not travel between different research communities. The individual must first be inducted into NOMINATE research protocols before he or she is able to correctly interpret the statistical arrays produced by the algorithm. If there were, in fact, a logical connection between the statistical artifacts produced by the NOMINATE system and the language deployed to interpret them, this induction would not be problematic; it would, as the NOMINATE community often insists, be training in a “science.” However, because there is no logical connection between the artifacts and the interpretation placed on them, the invitation to join the NOMINATE community is an invitation to adopt a subjective way of seeing the world that this community has culturally created. We may still want to do this, but our reason cannot be that the community has created a new and better “science.”

We now turn to how these social conventions and interpretive norms are created within the NOMINATE community. The first step is to insist, as we have done, upon the logical independence of (a) the NOMINATE algorithm as a statistical processor of data from (b) the assignment of meaning to the numerical coordinates and two-dimensional arrays it produces. This is not as easy as it sounds because the NOMINATE community has thoroughly identified the statistical artifacts produced by the algorithm with the meaning assigned to them by their social conventions. Distinguishing between the artifacts and that meaning requires that we carefully disentangle that identification.

We should start by reminding ourselves that the algorithm would produce coordinates and displays even if they were, in fact, meaningless. However, the NOMINATE community has generally insisted that the numerical coordinates and two-dimensional displays must mean something even when they disagreed on what they meant. As a result, there are many alternative explanations of what the coordinates and spatial displays might mean or represent, but almost no recognition of the fact that, as we shall see, the choice between meanings is essentially arbitrary in some cases and tautological in the rest.

The labeling of the points is often the critical interpretive decision made in NOMINATE analysis. For that and other reasons, we should begin with the bare coordinates and their associated two-dimensional array of points. For example, the points in a two-dimensional display can be denoted by letters indicating party identification (e.g., “D” and “R”) and the display would then ostensibly present an array of points representing Democrats and Republicans. We would then, in most instances, set about interpreting the array in terms of party programs or organizational loyalty. Alternatively, we could assign the points ideological labels (e.g., as determined by support scores for policy positions endorsed by the Americans for Democratic Action). The letters in the array might then be “L” and “C” for “liberals” and “conservatives.” We could create similar labels for the urban, suburban, and rural constituencies of the members; gender; region (e.g., North, South, Midwest, and West); or support or opposition for a presidential administration. We could do the same thing for the individual attributes of the members, such as age and hair color.

However, none of these alternative labeling possibilities resolves the basic question of whether or not the coordinates and the spatial displays have, in and of themselves, any inherent meaning in language.Footnote ⁸ When we base our interpretation of the displays on the labels we have adopted, we are often implicitly or explicitly importing meaning from outside the algorithm. For example, because we already know from studies that do not use the NOMINATE algorithm that political parties organize much of legislative policymaking, we might consider labeling the points “D” and “R” to be reasonable. On the other hand, labeling the points with the hair color of the members might seem senseless for the same reason. The important point is that, if we reason in this way, we are “importing” the rationale from outside the algorithm. There is nothing in the NOMINATE system that can direct us to a “correct” labeling decision.Footnote ⁹

Labeling is not only arbitrary. It is also surreptitiously deceptive because, once they are labeled, the points appear to represent stable facts. A point, for example, can be labeled “Democrat” if the member belongs to that party, and in one sense, the label is stable because that label always attaches to the point produced by the algorithm from the member's voting record. However, the point thus labeled is unstable in that it moves around in the two-dimensional display if the data set is modified by adding or subtracting votes or members. The stability of the label and the instability of the point cannot be reconciled (e.g., a member does not become more or less of a “Democrat” as a change in the data set moves the point around the display by altering the calculation of the numerical coordinates). Put another way, because the labels do not represent a property processed by the algorithm, they are stable. They are simply names attached to the points. However, the points themselves are not stable because they are a malleable product of how many and what kinds of votes are included in the data set.Footnote ¹⁰

Labels are thus theoretically distinct from and logically independent of the statistical artifacts produced by the algorithm. And for that reason, the visual conflation of labels with the points in the two-dimensional display conveys a misleading certitude with respect to the meaning of the points. And what is true of party names is also true of the individual whose voting record is processed by the algorithm. The individual is always the same individual and the voting record is always the same voting record, but the point produced by the algorithm is always conditioned upon (and thus partially produced by) the other individual voting records in the data set. In sum, labeling the coordinates and points in a NOMINATE display does not attach meaning to the statistical artifacts because the choice of labels is arbitrary, and, related to that fact, the labels themselves do not name properties processed by the algorithm. The only things processed by the algorithm are sets of binary data relative to other sets of binary data.

However, the NOMINATE community can assign meaning to these numerical artifacts and two-dimensional displays by creating definitions. When, for example, the authors identify one of the two-dimensional displays produced by the algorithm as “the first dimension,” they are creating a definition and thereby announcing that they will use the term in that way.Footnote ¹¹ There is no ambiguity here because the term merely describes a particular geometrical display and the algorithm will regularly and infallibly produce these displays.Footnote ¹² Similar definitions have been created, for example, for spatial distance, ideal points, and choice space. However, as we shall see in the next section, serious problems arise when we attempt to attach empirical meaning to these terms.Footnote ¹³

“PARTY POLARIZATION” AND THE NOMINATE SYSTEM

One of the most common terms in the NOMINATE system is “polarization.” The term, for example, plays a central role in Frances Lee's article in this symposium, in which she argues that NOMINATE coordinates demonstrate that political parties in Congress during the Gilded Age were highly polarized. However, she also contends that, even though the NOMINATE evidence reveals a statistical pattern that is conventionally labeled as “polarized,” the pattern (and thus the term itself) does not necessarily indicate that the parties were ideologically contentious.

As she notes, the conventional definition of “polarization” within the NOMINATE community

This is elegantly stated and correct as far as it goes. Let us, however, approach the issues Lee raises from a slightly different angle. The underpinning “assumptions” Lee describes are, as we have seen, themselves logically outside the NOMINATE system.Footnote ¹⁵ However, she accepts them insofar as they define a “choice space” in which partisan “ideal points” can be estimated. It is the empirical content of these ideal points that Lee contests because she maintains that party “polarization” during the Gilded Age was largely devoid of policy content and was therefore not ideologically organized or motivated. By dumping all roll calls into one data set, NOMINATE mixes together decisions that have policy content with those that lack such content. The result, Lee implies, is a statistical artifact that represents neither partisan nor ideological polarization.Footnote ¹⁶ If we were to separately calculate partisan ideal points on those decisions that involved the allocation of patronage, the seating of contestants in congressional elections, investigations of administrative malfeasance, and so forth, we would, Lee appears to contend, see that polarization was primarily driven by party competition for power and the distributive benefits of political victory. Lee thus contends that the NOMINATE algorithm can generate ideal points that can mean something but that the NOMINATE community has, in this instance, not been very careful in determining what that meaning might be.

Let us assume that we could divide all roll call votes into those that were ideologically organized and motivated and those that were solely intended to maximize the prospects for a party's victory in elections.Footnote ¹⁷ We would then have two sets of ideal points, one for the ideological data set and one calculated for partisan roll calls. At this point, we could ask Lee why the ideal points produced by the algorithm for one of these data sets should be regarded as more representative of political contestation in the Gilded Age than those in the other data set. The NOMINATE algorithm cannot give us an answer to this question. Lee herself can provide an answer only by referring to a larger, historical literature that, in fact, does not utilize the statistical artifacts of the algorithm.Footnote ¹⁸

But, again, that is not the important question. The important question asks what the ideal points mean even after the data sets have been purified by separating policy votes from partisan decisions. On the one hand, even a “purified” set of ideological roll calls can fail to include ideological issues that are clearly salient in national politics. For example, the House of Representatives was remarkably reluctant to vote on issues related to the Vietnam War during the early years of that conflict, even though large protests and demonstrations were occurring in much of the nation. Similarly, race segregation in the South produced almost no votes in Congress for long stretches of the late nineteenth and the first half of the twentieth centuries. On the other hand, party organizations can be polarized in terms of the policy positions they assume in national party platforms and yet be internally divided in Congress on those very same policies (because some of their members cast votes against those policy positions). If this were the case, the NOMINATE algorithm would again fail to pick up policy polarization.Footnote ¹⁹

In sum, despite Lee's best efforts, the statistical artifacts created by the NOMINATE algorithm will never align very well with ideological contestation between the parties in empirical reality. In response, we might attempt to recalibrate the data set in some way so that it accurately reflects ideological contestation actually taking place in the nation at large. How the analyst might do this without abandoning any possibility that the NOMINATE algorithm might produce something meaningful with respect to ideological polarization is not at all clear.Footnote ²⁰ At this point, an insistence that the NOMINATE algorithm can be useful as a measure of ideological polarization between the parties might appear rather fetishistic.

But there is an even more fundamental problem with respect to the relation between the coordinates the algorithm produces and their representation as aspects of empirical reality. What does the algorithm empirically reference, for example, when the party coordinates are closer together or further apart? We could define the former as “less polarized” and the latter as “more polarized,” but, as is true of all definitions, this would be a tautology (and, as tautologies go, a rather unsatisfactory one in that the coordinates would move further apart or closer together depending on the inclusion or exclusion of votes in the data set).Footnote ²¹

But this is part of the broader problem that has already been discussed: If we cannot logically connect NOMINATE coordinates and spatial displays to language, these statistical artifacts cannot be integrated into historical analysis. As it stands now, NOMINATE analysts essentially point to statistical arrays produced by the algorithm and say “look at this.” That is profoundly not a Wittgensteinian moment in which we, as viewers, confront the brute, irreducible reality of the world.Footnote ²² And, for that reason, the yawning chasm between the nature of the NOMINATE system's statistical artifacts and their potential utility in historical analysis is still as wide as ever.

INTERPRETATION OF THE FIRST DIMENSION AS IDEOLOGY

Lee appears to be making two separate points with respect to the relation between ideology and the NOMINATE system. On the one hand, she contends that the major political parties rarely engaged in ideologically driven policy conflict during the Gilded Age, and thus the statistical artifacts produced by the algorithm cannot be measuring ideological beliefs during this period. As a result, party polarization (which is defined within the NOMINATE system and subsequently revealed by the numerical coordinates generated by the algorithm) cannot have originated in ideological conflict. On the other hand, she also proposes that NOMINATE coordinates sometimes indicate ideological conflict and sometimes do not, depending on the type of policy or policies under analysis.Footnote ²³ These two points are, of course, related in some ways, but the first is a substantive claim about the nature of public policy during the Gilded Age, and the other is a theoretical claim concerning the relationship of the algorithm to political reality—whether the first one is true or false is independent of whether the second is true or false. However, both claims require that “ideology” be clearly defined. In order to know whether or not most partisan competition was ideologically driven and whether or not NOMINATE coordinates can, potentially at least, indicate ideological belief, we first need to know what ideology is.

Lee avoids the task of defining ideology by maintaining that partisan ideological alignments can only be revealed by policy differences, and since there were no policy differences between the parties in the Gilded Age, the major parties could not have been ideologically polarized.Footnote ²⁴ However, she nonetheless recognizes that most research using the NOMINATE system does contend that the numerical coordinates usually, if not always, indicate ideological sentiment.Footnote ²⁵ In fact, Keith Poole and Howard Rosenthal, the creators of the algorithm, entitled their major treatise Ideology & Congress. In that book they define ideology in this way:

However, as Bateman and Lapinski correctly observe, the definition of ideology adopted by Poole and Rosenthal is not compatible with the conception that Converse proposed.Footnote ²⁷ And because Poole and Rosenthal do not provide any other definition of ideology, the ostensible link between ideology and the statistical artifacts produced by their algorithm is, by default, tautological. They say as much on the first page of Ideology & Congress: “The spatial model of voting … is the technical foundation of our model. For short, we refer to it as the ideological model.”

However, Poole and Rosenthal do state that the “clusters” that appear on the two-dimensional displays produced by the algorithm “basically” represent “conflict over economic redistribution” and, by implication, that this conflict is synonymous with ideologically organized struggle.Footnote ²⁸ This claim is inductive in the sense that it arises out of a superficial and clearly selective examination of the policy issues that have generated the visual displays they reproduce in their book. This inductive process ensures that the patterns must conform to their conception of ideology, because the arrays, in fact, define what ideology means. Thus, as Bateman and Lapinski correctly note, “the conceptualization of ideology in DW-NOMINATE has no intrinsic or stable connection with policy positions.” They also note that Poole and Rosenthal have referred to “the two-dimensional space in a number of different and not entirely compatible ways” in various publications, including ideology, party loyalty, and as “part of the ‘perceived reality’ of contemporary America.”Footnote ²⁹

Bateman and Lapinski go on to say that “the labels ‘liberal’ and ‘conservative’ … entail issue positions” and that “to characterize” the numerical coordinates in this way risks anachronism, “especially for periods in which liberalism and conservatism labels might be less relevant axes of political alignment.” They then discuss the voting record of Mississippi Democrat Samuel A. Witherspoon (1911–15), asking whether it makes sense to say that he was more or less liberal than Dennis Kucinich or Adam Clayton Powell, Jr.Footnote ³⁰ All of what they say is correct, but the more important point is that the conventional interpretation of NOMINATE coordinates treats liberalism and conservatism as trans-historical ideals that guided the alignment of members of Congress even when the very terms as labels for political attitudes were unknown to them. For example, in the early nineteenth century, members of Congress would have been at least bemused to find that their policy positions were somehow unconsciously shaped by an ideological alignment that has its primary roots in the New Deal.Footnote ³¹

But the problem goes beyond mere anachronism because the notion of a trans-historical alignment also contradicts our current understanding of ideology. This becomes clear if, for example, we were to compare the voting records of William Jennings Bryan (Democrat of Nebraska) and William McKinley (Republican of Ohio).Footnote ³² In a two-dimensional display produced by the NOMINATE algorithm, Bryan's ideal point would be found far to the left of McKinley's, with both of them securely ensconced in the huddles composed of their respective party colleagues. After inspecting this display, the NOMINATE analyst would conclude that Bryan's ideology was “very liberal” while McKinley was “very conservative.” What does it actually mean to say, using the NOMINATE algorithm, that Bryan was much more liberal than McKinley? In the first instance, all that the statement means is that the numerical coordinates produced by the NOMINATE algorithm place Bryan a relatively large distance to the left of McKinley on a two-dimensional display.Footnote ³³

The contradiction with our current understandings of ideology can be attributed to the profoundly anachronistic assumption that “liberal” and “conservative” ideologies meant the same thing in the late nineteenth century as they do in our own time. This is easily demonstrated when we recall Bryan's opposition to black suffrage in the South and consistent support for individual state sovereignty in most policy areas. McKinley, on the other hand, voted the other way on these things.Footnote ³⁴ However, we would commit the same error if we tried to maintain that Bryan was really a conservative or that McKinley was really a liberal. The fact is that whatever ideology might mean over the course of American political development, it must be historically contextualized. NOMINATE analysts, instead, usually assert that the algorithm has (somehow magically) converted all contextual historical experience into a single metric, and that the content of that metric (in terms of what ideology actually is) can only be revealed through an examination of the coordinates the algorithm produces.Footnote ³⁵ That assertion more resembles a spiritual belief than it does a serious analytical claim.

Bateman and Lapinski still hold out hope that NOMINATE coordinates might better “approximate ‘ideology’” if “more information” were “integrated into the estimation procedures.” They suggest, for example, that “ratings from external organizations” or “the written opinions of newspaper editors and columnists” might be projected “into the same space as members of Congress” and thus “more precisely capture what is meant by liberalism or progressivism.”Footnote ³⁶ Caughey and Schickler proceed somewhat differently, arguing that the conventional claim that

Their argument proceeds in three steps. In the first, they contend that NOMINATE coordinates must reflect ideology because they correlate well with the roll call ratings published by the ADA and the ACU. Then they note that there are imperfections in those roll call ratings. In the final step, they then conclude that NOMINATE scores must thus be even better than ADA and ACU roll call ratings. The first step is correct: The correlation is usually high. The second step is also correct: The roll call ratings are imperfect. However, the final step cannot be deduced from the first two for a number of reasons.

For one thing, the high correlation between NOMINATE coordinates and ADA/ACU ratings does not imply that the former are ideological in character. It simply means that they correlate. A lot of things, in fact, correlate with roll call ratings, but they are not inherently ideological in character. But, more importantly, the authors assume that the imperfections attending calculation of the NOMINATE coordinates are less debilitating than those associated with roll call ratings. How would we know that, unless we independently knew what ideology was and were thus in a position to compare NOMINATE coordinates and roll call ratings to that notion of ideology?

As noted earlier, Lee points out that the indiscriminate mixing of “partisan” and “policy” issues in the NOMINATE system makes mush of the coordinates as a means of assigning meaning to “party polarization.” For the same reason, the indiscriminate mixing of ideological and nonideological issues makes mush of the coordinates as a means of assigning meaning to “ideology.” We could attempt to separate out ideologically constructed issues from the other roll calls, but that would require a conception of ideology independent from the coordinates. And if we had that, we would no longer need either roll call ratings or NOMINATE coordinates. The basic problem is that most NOMINATE users want to use the coordinates to assign ideological labels to members without defining or otherwise specifying the content of ideology.Footnote ³⁸ If we knew what ideology was (e.g., how policy decisions could be interpreted on an ideological spectrum), we could place roll calls on the left–right dimension (so forming a scale) and thus place legislators on a line after examining their voting records. If we do not know what ideology is, we cannot do this—and we cannot do it with the NOMINATE coordinates as well. There is no mysterious alchemy in the algorithm that somehow allows us to perceive and thus recognize ideology when we cannot otherwise comprehend it. And if we can independently comprehend it, then it is the NOMINATE coordinates that should be interrogated to see whether or not they represent the ideological predilections of members of Congress.

Before moving on, we should also note that there is at least one sense in which the ADA or ACU ratings cited by Caughey and Schickler are much more meaningful than NOMINATE coordinates, and that is because members of Congress, as well as those who rate them, actually pay attention to them. Although ADA practice has since changed, for years legislative staff serving members belonging to the liberal wing of the Democratic party selected the votes used in ADA ratings. They were politically informed and certainly had some feel for the corridor politics in their respective chambers. When used to construct an ideological measure, the selection of roll calls by these staff members was actually dictated by “practical politics,” not the application of abstract principles to policy alternatives. As Linda Fowler put it,

As one ADA official confessed, “Somehow on the Hill, liberalism and conservatism is an experienced fact, but how it happens is mysterious. Lobbyists, legislators, and their staffs interact and modify each other's views in a triangular process. We all take cues and give cues.”Footnote ⁴⁰ Ultimately, it is the evolving social and political relations constituting these groupings of people who have declared themselves to be liberals or conservatives that determine the policy meaning of ideology.

Noting that someone “needs to process the chaos of the world into ideological order,” David Mayhew describes “the Capitol Hill community [as] a kind of collective Madame Defarge, weaving day after day an ideologically ordered tapestry out of whatever material comes in.”Footnote ⁴¹ More than forty years ago, Converse similarly described this process, noting that

In these passages, Mayhew and Converse have suggested a very different conception of ideology from the conventional notion resting upon individual beliefs. Since this socially produced understanding of ideology is radically different from the individualist notion underlying most interpretations of NOMINATE coordinates, let us take a moment to set out how this alternative conception might be constructed.

When viewed as a socially produced feature of politics, ideology becomes a set of cultural values exhibited, shared, and mutually understood by members of a self-identified group (as opposed to individual beliefs organized and disciplined by a logically ordered system deducible from abstract principles). There are several empirical and theoretical advantages to such an interpretation. For one thing, these cultural values would be, in a sense, suspended between the members of a self-identified group in such a way that (a) they would be collectively shared among the members of the group without requiring that a member either be cognizant of all the values (e.g., an individual could belong to a group without being aware of or otherwise subscribing to all of the group's values); (b) individual members of the group could serve as exemplary bearers of these values in such a way that their actions alone (not the logic of their explanations for their actions) could create or substantiate these values; (c) individuals would, in that sense, take cues from other members of the group when taking a political position (as opposed to making a decision by referring it to an internal, personal belief system); (d) over time, the trajectories of individuals and their groups would influence their identities in the sense that individuals could move between groups, thus changing both their own political identity and the composition of the groups that they left and the ones that they joined; and (e) that would mean that the cultural values associated with any particular group would “drift” over time, in some instances even coming to assume values that contradicted those that had been held sometime in the past. All of these are interpretive advantages insofar as they better explain how (what is conventionally termed) ideology has actually operated in American politics.

In the absence of an explicit conception of ideology as a logically deductive system derived from theoretical first principles, “liberalism” and “conservatism” are thus tribal insignia as much as they are representations of formally defined belief systems.Footnote ⁴³ As a result, those who calibrate the ratings carefully select the roll calls so that their friends and allies in Congress are assigned very high (often perfect) scores.Footnote ⁴⁴ Because both staff members and the members they serve calibrate their behavior so as to be awarded these very high scores, ADA ratings have shaped “social reality” on Capitol Hill, even though they are suspect as representations of ideological belief systems. In rather sharp contrast, there is no evidence that any member of Congress has ever tried to manipulate their NOMINATE coordinates by changing their position or abstaining on a roll call. The algorithm's statistical artifacts are thus inferior to interest group ratings both as representations of ideological belief and as influences shaping the social reality of members of Congress.Footnote ⁴⁵

Assuming that the ratings of organizations that monitor congressional voting can and actually do represent ideological beliefs arising out of the practice of politics, should the ideological scales that they publish (a) be interpreted in their own historical context as referencing beliefs that developed out of specific political conflicts (and thus have meaning primarily within those conflicts) or (b) be discarded in favor of a trans-historical spectrum of left–right, liberal–conservative belief systems whose influence on political actors can be detected from sheer patterns of political behavior even if the guiding principles of these trans-historical ideologies remain unknown? The first option privileges the particularity of historical conflict and the explicit understandings of political actors in their own time. It is inductive in that we must gather the necessary evidence before reconstructing ideological belief. Only after reconstructing that belief should we attempt to create ideological scales out of roll call votes. The second of these (i.e., the brute imputation of ideological content upon NOMINATE coordinates) is deductive in that the construction of the algorithm and the calculation of the coordinates precedes (and often substitutes for) historical research.

The first option asks what political actors actually believed within a particular historical period, including the possibility that those beliefs might have been logically inconsistent in some respects. The second imputes beliefs to political actors by assuming that those beliefs can only be revealed through statistical analysis and, because policy content is irrelevant, cannot detect whether or not ideological beliefs may have been, at least in part, logically inconsistent. With respect to this narrowly framed set of interpretive possibilities, Caughey and Schickler prefer historical contextualization. Although they do not explicitly identify inconsistencies in the way progressivism was constructed in the 1920s, the possibility is implicit in their description of the heterogeneous progressive coalition of the 1920s.Footnote ⁴⁶

METHODOLOGICAL INDIVIDUALISM AND NOMINATE TERMINOLOGY

As is the case with much of the contemporary literature on legislative behavior, research utilizing the NOMINATE algorithm rests almost exclusively on methodologically individualist assumptions. Members of Congress, for example, are assigned coordinates as individuals, and these coordinates are interpreted in terms of individual attributes such as ideological beliefs, loyalty to a particular party, alignment with a regional bloc (such as the Southern Democrats of the 1950s), or attitude toward racial segregation. As a result, roll calls are interpreted as representing the independent calculations of individual members who decide how to vote after assessing such things as the ideological content of a policy, the expectations of their constituents, the position their party has taken, the opportunities for logrolling with colleagues, and so forth. That individual members are often autonomous agents as they participate in the legislative process is an entirely safe assumption, well-documented in primary research. However, each of these contexts in which they operate as autonomous agents entails relationships that embed the member in a social community.

For example, the member often, if not usually, evaluates the ideological content of a policy proposal in terms of how other members, interest groups, and constituents interpret the proposal. The assignment of an ideological label to a policy is thus a socially constructed decision (in part because ideology is at least as much the product of group membership as it is a logically deductive, formal theoretical system). Similarly, constituents communicate their desires to the member who then must balance the conflicting requests they present. The persuasive authority of the party leadership and the negotiations attending log-rolling proposals are likewise social in nature. The individual member of Congress is thus suspended in a web of social relationships that (a) create the context within which the member evaluates policy content, (b) confer a public identity in the home district, (c) modulate his or her standing within the party caucus, and (d) give rise to the member's reputation as someone who is both willing and able to broker competing legislative priorities.

The language, concepts, and interpretations associated with the analysis of roll call voting in the NOMINATE community reduce all this complexity into the personal calculations of legislators, individuating their thoughts, beliefs, and actions from those of other members. This atomization suppresses study of the linkages between members, including hierarchical relations between leaders and followers, mutual cooperation between members within small groups, the emergence of shared understandings and interpretations in the legislative arena, and the detection of reciprocal cooperation across policies. Because the radical individualism of the theoretical model assumes an equality of influence and an autonomy of decision across all individual members, it distorts our understanding of the process through which legislation is crafted. Most importantly, the actually quite demanding assumption that members carry a fully elaborated ideological belief system into their necessarily cooperative and group-oriented legislative deliberations simply misconstrues the way in which members mutually construct and act upon their policy preferences.

The concept of an “ideal point,” for example, theoretically strips a member of all interpersonal, cooperative (or competitive) relations, reducing policy choices to individual selection from a universe of objectively defined possibilities.Footnote ⁴⁷ The fundamental problem with this concept again concerns language. In order to be used in historical analysis, we must know what the labels applied to the statistical products of the algorithm actually mean. From that perspective, we must ask: What is an ideal point? We can certainly identify it as a statistical artifact plotted as a dot in a two-dimensional frame, but what is its meaning in language (and, thus, in historical research)? One answer might be that an ideal point sums up all the factors that give rise to a member's policy preferences and, thus, identifies an equilibrium in which all the conflicting demands on the member are in some kind of balance.

Using rational choice terminology, we can restate the conventional definition of an ideal point more formally as representing that bundle of goods that maximizes the utility of an individual in a particular setting (the setting determining the choices available to the individual).Footnote ⁴⁸ We must then identify the setting. Let us load the dice by making the setting Congress and then stipulating that the procedural rules and knowledge of the preferences of the other members (we would need all of that) determine what sets of choices are available to individual members (not all conceivable policies, for example, but only those that are presumed to be possible in some sense). The ideal point for a member of Congress might thus be the maximization of utility with respect to the bundle of possible policies that might come before the institution during a given session.Footnote ⁴⁹ A curious analyst might then ask three questions about this ideal point:

1. 1. Can an ideal point be identified outside of the algorithm that produced it (say, by evidence from the political life, thoughts, or public speech of the member combined with a thick historical description of the institutional context within which he or she made choices)? In other words, does it correspond with something else in the political record that might independently support the interpretation of the statistical artifact as an ideal point?

2. 2. Is the member aware of his or her own ideal point? This is highly unlikely because, among other things, the future contains, at any point in time, at least some of the things in the bundle. If the member could accurately predict the future (i.e., possessed perfect information with respect to future policy opportunities and choices), this would not be a problem.Footnote ⁵⁰ However, the member cannot accurately predict these things. We can certainly say that a member attempts to roughly anticipate what might happen with reference to future policy decisions but that rough anticipation is emphatically not the same thing as an ideal point.Footnote ⁵¹ And if we are attributing something to a member of which he or she is unaware, what is that something? And how does an ideal point determine member behavior if, as we might colloquially surmise, it only lurks in the member's unconscious or, perhaps more charitably, intuitive feel for a situation? Put another way, what does that plotted point mean if the member it purportedly represents cannot consciously comprehend an “ideal policy bundle”?

3. 3. Do all members of Congress or political actors in general make choices solely on the basis of their personal utility arising out of those choices? On this last point, we might reasonably ask: Aren't some members “followers” of other members (we would then label the latter “leaders”)? In extreme cases, would not the ideal points of these followers become identical with (or at least heavily influenced by) those of their leaders? Even if this were only the case with respect to some of the choices presented to a member, wouldn't the conception of an individual ideal point become distorted beyond all recognition?Footnote ⁵²

Within the NOMINATE system, the ideal point that identifies the balance between competing legislative alternatives is often defined as the ideology of the member. Bateman and Lapinski are well aware of the problems associated with using roll call records to identify such an ideological ideal point and recommend that NOMINATE coordinates be calculated for subsets of roll calls on related issues. They illustrate their argument by comparing the relatively liberal results that J. William Fulbright of Arkansas would earn on foreign policy with the very conservative coordinates he would be assigned on civil rights (pp. 163–164). While their suggestion is well-intended, there are several problems with their recommendation.

First, NOMINATE coordinates would no longer represent a member's unified worldview because he or she would have many ideologies, each one computed over a different subset of roll calls. It is not at all obvious what a many-ideologies theoretical framework would look like. Second, nominally identical policy decisions should not be placed in the same issue subset if they were recorded in very different historical periods. In fact, the placement of a policy in an issue category is often problematic even in the same historical period. Is abortion, for example, a civil liberty deducible from a right to privacy or a criminal act because it entails the taking of life? While such difficulties might sometimes be evaded by constructing categories that encompass both possibilities (and, thus, the analyst would not have to choose between them), they make a mockery of the concept of ideology itself, which necessarily recognizes that the construction of a policy decision by the member is a profoundly moral act, not something immanent in the natural world. In general, we should accept that the construction of any classification scheme for policy issues is not a discovery of an immanent order somehow residing in social reality but, instead, rooted (at best) in historically contextualized understandings of how policies fit together or (at worst) ideologically grounded interpretations of the correct way of sorting individual issues into categories.

In order to be integrated into historical analysis, an ideal point must be capable of translation into language. Since it cannot be so translated, this statistical artifact is fatally flawed. We more or less concede this flaw when we admit that individual members cannot comprehend their own ideal points as they legislate. This is not just because the comprehension of all the potential policy bundles at a given point in time is simply beyond the capability of the member. And it is not just because the future is both relevant to these bundles and radically uncertain, or that some members lead and other members are led. It is because the NOMINATE system simply cannot state, in language, what the statistical artifact represented by the plotted dot actually is in terms of politics. Put another way, ideal points are not ideal representations of anything in historical or political reality. Whatever meaning can be assigned them is solely the product of the social conventions that have arisen within the NOMINATE community.Footnote ⁵³

SOME ADDITIONAL THOUGHTS ON THE RELATIONSHIP BETWEEN LANGUAGE, NOMINATE, AND HISTORICAL ANALYSIS

Historical analysis differs in several ways from mainstream study of political behavior. For one thing, the social context of political action changes over time, so that what appears on the surface to be the same behavior in two historical eras in fact conveyed a very different meaning for both the actors and those who monitored their behavior. For this reason, we, as modern day analysts of historical behavior, must be aware of a potentially misleading reliance on empathy as a guide or framework for interpreting political action in the past. Because the social context of the past is different, our own psychological presumptions and calculus of decision making are not the same as they were for the people who we choose to study. We should be eternally wary, for example, of an interpretation of historical behavior that begins with “a reasonable person would have chosen to do X,” in which that reasonable person is not historically contextualized. One of the most important preconditions for historical political analysis is thus the re-creation of the self-understanding of individuals as they participated in politics. In this section, I want to examine two issues: (a) the relation between the casting of a vote and the intention of the voter and (b) the relation between the language in which we describe the link between vote and intention, on the one hand, and the statistical apparatus in which we evaluate that link.

The recorded vote in Congress is the unit of analysis that constitutes the very foundation of the NOMINATE system. In one sense, roll call votes in Congress may be the most empirically well-defined and certifiably evidenced acts in all of politics. Their exactitude as empirical facts arises as the intentional product of the highly formal settings in which they are recorded. As institutionally recognized preferences, Congress has laid down rules and precedents that specify when, where, how, and by whom votes may be cast. Members are simply ignored if they do not conform to the ritual forms set out in these rules and precedents. For example, a member who attempts to cast a vote when another member's name is called may audibly announce his or her preference, but the institution (more specifically, the ritually designated officer whose task it is to record votes) will ignore that declaration unless it is announced at the proper time (i.e., after the member's name is called). However, whether a member shouts out a vote or sends a written note to the front desk does not matter. Nor does it matter if a member prefaces his or her vote with oral commentary or simply states his or her decision. In these and other ways, the institution strips the casting of a vote of everything that is considered to be extraneous to the precise enumeration of formally eligible preferences.

The casting of a recorded vote in Congress is thus a profoundly socially constructed act, one of the most thoroughly policed behaviors in all of human society. And, for that reason, members are rapidly and universally disciplined into conformance with such institutional rules and practices. As a collateral benefit of their formality, we are presented with a data set of unsurpassed exactitude.Footnote ⁵⁴ And the formal rules, precedents, and practice of Congress have succeeded in eliminating almost all of the variation in these votes that might otherwise be introduced by differences in historical context.Footnote ⁵⁵

However, the socially constructed exactitude of the recorded vote in Congress emphatically does not imply that we know what the individual member intended when he or she cast a vote.Footnote ⁵⁶ This intention can (and does) vary in at least three dimensions: personally (when the intention of the voter varies across different votes), contemporaneously (when the intentions of voters vary from one voter to another in the same Congress), and longitudinally (when the intention of voters varies across historical eras). The task of historical analysts is to determine, as best they can, what the motives of a member might have been when he or she cast a roll call vote and, thus, what meaning should be attached to that vote. In some contexts, the decision at stake might have had profound implications for the electoral fate of a major party. In others, the policy might have carried very important distributive benefits for the districts of some members and been all but inconsequential for the rest. Ideology, in the sense of normative understandings of what kind of country the United States was to become, may have motivated the casting of votes in other cases. And these things mattered across all three dimensions: individual members simultaneously held and hold ideological, partisan, and constituency interests to which they responded when they voted; the motives of members vary within a single vote; and motives certainly varied across historical eras.

The reason that a roll call vote is so exactly and unambiguously recorded is precisely because all of its social conditions and contextual requirements are set down in a language that all the members share and understand. There is thus a one-to-one correspondence between a vote (as a unit of analysis) and its description as one of many particular behavioral acts. There is, however, almost always a sizable gap between an individual member's intention when that vote is cast and what we know of that intention. Closing all of that gap is impossible, but we can narrow the discrepancy by paying close attention to the historical context of a decision, the identity of the member, the leader–follower and social relations in which the member participated, and the personal reports of the member. Or, alternatively, we can widen that gap by using the NOMINATE system.

As several of the contributors to this symposium have noted, the NOMINATE algorithm merges all member votes into the same data set. When the statistical artifacts produced by the algorithm are interpreted, the analyst selects, more or less arbitrarily, which meaning to assign to the votes as if all the members shared a common motivation in casting them. But that point has already been made. The important point here is that unparalleled exactitude of the units of analysis in the roll call data set has been more than equaled by the almost unrivaled imprecision of their interpretation within the NOMINATE system. This is where language comes in.

Because language is the medium through which we construct and navigate the social world, the social relations and political decisions in which members of Congress participate have no meaning outside their statement in language. In fact, they cannot even be conceived in the absence of language. In order to see that this is also true of statistics, we should begin by examining the relationship between a hypothesis and its corresponding statistic. A hypothesis is a precise statement in language that (1) describes the relevant evidence in empirical reality, which, in turn, implies (2) the statistic that evaluates how well that language describes empirical reality. If we cannot state the hypothesis in language, then we cannot interpret what it represents in empirical reality. And if we cannot state the evaluating statistic in language, then we cannot link it to the hypothesis and, thus, to a description of empirical reality. We must therefore be able to intertranslate between the hypothesis and the evaluating statistic, establishing a one-to-one correspondence between the relations it describes in empirical reality and the relations evaluated by the statistic.

For example, consider the following hypothesis: “In this jar containing black and white marbles, there are at least twice as many black as white marbles.” In evaluating whether or not this statement is accurate, we would count the marbles and calculate their respective proportions of the total. That would be the sense in which the hypothesis implies the statistic (in this case, a very simple mathematical operation). Traveling in the other direction, the statistic implies the form (but not the specific content) of a hypothesis. In this particular example, the statistic (i.e., the calculation of proportions) would be appropriate for all those hypotheses in which counting and proportions were entailed in determining the relation between the hypothetical statement and its manifestation in empirical reality. The point I want to make is that the NOMINATE algorithm does not correspond to the statement of any empirically relevant hypothesis and, thus, cannot evaluate the relation between any hypothetical statement and its manifestation in empirical reality.

The NOMINATE algorithm can certainly be stated in language (including the corresponding mathematical symbols). However, the NOMINATE algorithm does not represent anything in social reality because it does not correspond with an empirically meaningful hypothesis.Footnote ⁵⁷ In the absence of such a correspondence, NOMINATE can only generate statistical artifacts that have no meaning in social reality.Footnote ⁵⁸ The problem is not that the sophistication of our language has not caught up with the statistical techniques employed in the construction of the NOMINATE algorithm. The problem is that the NOMINATE algorithm and its several variants have evolved independently of the language we must rely upon to describe and interpret social reality. Our fascination with the statistical artifacts that the algorithm produces has then dragged language in its train, creating terms and notions that have standing only within the social conventions of the attending interpretive community.Footnote ⁵⁹ Those social conventions, however, merely cloak the fundamental problem: the absence of a correspondence between the algorithm and the social world whose empirical content it purports to represent.