Abstract
Many standard models of political institutions frame outcomes as a function of the preferences of key decision makers. However, these models, and the empirical analyses they inspire, typically assume decision makers can infer the identities and ideological locations of other decision makers without error. Here, we reveal the substantive importance of this assumption. We show that partisan sorting, a common cause of polarization, can result in reduced uncertainty about the ideologies of key decision makers and the identities of key pivots. When we incorporate estimates of pivot uncertainty into empirical models of executive order issuance, we find lower levels of uncertainty are associated with higher rates of policy-relevant executive order issuance. These results have implications for the study of polarization and the use of models of institutions in political science.
Over the past several decades, elite polarization in the United States has steadily increased, with individuals sorting into parties based largely on ideological lines; liberals have become more aligned with the Democratic Party, and conservatives with the Republican Party (Bafumi & Herron, 2010; Fleisher & Bond, 2004; Layman, Carsey, & Horowitz, 2006; McCarty, Poole, & Rosenthal, 2006). Within the halls of Congress, these dynamics are reflected in historically high rates of party support scores, party unity votes, party unanimity votes, and growing ideological divergence between the two parties. Recently, it has become far easier to predict how individual members of Congress will vote—as well as their ideological preferences—based on their partisan affiliations (Theriault, 2008).
Several causes of Congressional polarization have been proffered, including party influence (McCarty, Poole, & Rosenthal, 2001), demographic shifts (Aldrich, 1995; Fleisher & Bond, 2004), electoral polarization (Abramowitz, 2010; Abramowitz & Saunders, 2008), gerrymandering (Carson, Crespin, Finocchiaro, & Rohde, 2007; Fiorina, Abrams, & Pope, 2006; McCarty, Poole, & Rosenthal, 2009; Theriault, 2008), increased strength of parties (Cox & McCubbins, 2005; Theriault, 2008), the discouragement of ideological moderates from running for office (Thomsen, 2017), and polarization within Congressional leadership (Heberlig, Hetherington, & Larson, 2006). However, despite the interest in the topic, studies of the effects of polarization in the separation-of-powers context tend to focus on polarization as it relates to the ideological distance between the two parties, despite evidence that greater ideological divergence is not the only effect of polarization; indeed, polarization is also associated with greater intraparty ideological homogeneity, and not all members of Congress are equally affected by this latter factor. While ideological extremists might welcome stricter ideological dogma, moderate members may balk at supporting policies with which either they or their constituents disagree. On many votes, regardless of how these “cross-pressured” legislators vote, they may face condemnation from their constituents or party leadership, or they may find themselves supporting a bill with which they disagree. Thus, it is no surprise that increasing polarization has corresponded to a decline in the ranks of these inherently unpredictable cross-pressured legislators (Han & Brady, 2007). 1
Importantly, these cross-pressured legislators have been largely replaced by those whose ideological preferences more closely match those of their parties and the partisan members of their reelection coalitions (Han & Brady, 2007). As these members feel fewer conflicts between the demands of constituents, parties, and personal beliefs, voting records in more recent Congresses have more closely reflected the wishes of parties (Ramey, 2015). Moreover, with fewer cross-pressured legislators, “waffling” in Congress has decreased, with fewer members voting against bills they once (co-)sponsored (Kirkland & Harden, 2016). All of these dynamics have resulted in Congressional behavior becoming more predictable on the basis of partisanship alone (Theriault, 2008).2,3,4
We show partisan polarization induced by partisan sorting can result in greater certainty about the identities and ideological locations of key members of Congress. After showing this, we provide one example of this dynamic in the separation-of-powers context and show that, by our measures, uncertainty is associated with fewer executive orders. As mentioned, this is presumably because the president will have more information about the preferences of and/or identities of key players and will be able to structure executive orders in ways acceptable to at least one relevant pivot, thus preempting Congressional opposition.5,6 Moreover, uncertainty matters even when we incorporate the ideological divergence between the parties (i.e., one common way of operationalizing polarization) into our empirical models, a finding that should incentivize scholars to refine understandings of polarization and the effects thereof. 7
Polarization, Uncertainty, and Executive Orders
Despite the relationship between polarization and ideological uncertainty, the latter has yet to be seriously engaged by scholars of American institutions (e.g., Cox & McCubbins, 2005; Krehbiel, 1998; but see Cameron, 2000). This is despite the fact that greater certainty about the ideological preferences of key actors should affect institutional outcomes. Indeed, vast amounts of research in political science—and cognate disciplines—based in part on formal models of incomplete information have suggested that uncertainty is important to political interactions, and can change the incentive structures and actions of those involved. For example, private information about—and incentives to misrepresent—one’s military capabilities and willingness to fight have been cited as reasons for the occurrence of war (Fearon, 1995). Within American politics, it has been argued that one reason for the existence of political parties is their ability to reveal information about the preferences of those running under their labels (Snyder & Ting, 2002). Voter uncertainty over the president’s preferences can lead Congress to write bills it expects the president to veto, with the goal of making the president seem more extreme (Groseclose & McCarty, 2001; but see Martin, 2012). And uncertainty over the location of the veto pivot has been argued to provide the president more leverage compared to a world without uncertainty (Cameron, 2000).8,9
In particular, Cameron’s (2000) logic is that when individuals are less certain about the ideological locations of key pivots—or the identities thereof—it will be more difficult to structure bills to ensure that they will later be acceptable to the veto pivot. This same logic would suggest that if presidents are more certain about the identities and ideological locations of key pivots, they will be better able to structure executive orders in order to preempt legislative retribution. And this potential ability to use informational advantages to sidestep Congressional opposition is, in some ways, not altogether different from other sources of presidential advantages in the inter-branch bargaining process. For example, Howell (2003) argues that when Congressional policy preferences are broadly fragmented, Congress is unable to form majorities necessary to overcome subsequent vetoes of legislation introduced to negate executive orders—assuming they can even pass the negating legislation in the first place. 10 The common thread between these two dynamics (Congressional fragmentation and certainty about the ideologies or identities of key pivots) is that both might be caused by higher degrees of partisan polarization.
However, the extant research on executive orders has focused primarily on the first dynamic and variations thereof (such as the degree of ideological divergence between the two parties), and has largely ignored how growing partisan polarization might relate to ideological certainty. This is a notable oversight, given standard models of ideological sorting, and much empirical research on the topic suggests that the parties have not only grown further apart—to the extent that there is no longer any ideological overlap between them—but their ideologies have become more tightly concentrated around more divergent party medians (Bafumi & Herron, 2010; McCarty et al., 2006). These dynamics have consequences for the roles of Congressional fragmentation and certainty about the ideologies or identities of key pivots (due to increased intraparty homogeneity), and thus attendant consequences for executive order issuance patterns, as standard models assume the executive considers the preferences of the legislature before issuing executive orders (Cameron, 2000; Cameron & McCarty, 2004; Chiou & Rothenberg, 2014, 2017; Hassell & Kernell, 2016; Howell, 2003; Martin, 2012; Mayer, 2002; Tsebelis, 2002; Warber, 2006).
Within these standard models, of which Howell’s (2003) is perhaps the most prominent and well-known, executive orders offer the president an important advantage and an opportunity to take an active role in the creation of policy. However, within Howell’s (2003) model, this ability is limited and subject to discretionary limits imposed by the judiciary (wherein the judiciary will overturn the executive order if the discretion is exceeded), as well as limits on discretion—and possibly direction—imposed by the legislature. 11 Chiou and Rothenberg (2014, 2017) build on Howell’s model and formally introduce the role of parties, finding that models incorporating the majority party median exhibit better statistical fit than those where the executive is most responsive to the chamber median (or not responsive to any legislative actor).
That parties should condition executive order issuance behavior is not new; indeed, Marshall and Pacelle (2005) found that greater partisan divergence is correlated with fewer executive orders, all things considered, although their results vary depending on whether one examines executive orders related to domestic versus foreign policy. Instead, Chiou and Rothenberg’s key insight—at least for the purposes of this article—was the development of a theoretical rationale for why parties might matter to the executive order issuance process. But even despite this advance, parties only enter into their formal model in the form of the ideological position of the majority party median—as well as quantities based on the distances between this legislative actor and others (e.g., the distance between the majority party median and the veto pivot). That is to say, while the central tendencies of the parties are certainly relevant, neither Chiou and Rothenberg (2014, 2017) nor Howell (2003) consider the possible import of the ideological variances thereof, nor how they might relate to ideological uncertainty and/or executive order issuance. Here, using the logic of partisan sorting and marrying it to the intution underlying Cameron’s (2000) model of veto bargaining (in particular its incorporation of the importance of uncertainty), we show that ideological uncertainty also matters.
Partisan Sorting and Polarization-Induced Certainty: A Simulation
We first use a brief simulation to illustrate our argument regarding the relationships between partisan sorting, interparty ideological divergence, intraparty ideological homogeneity, and political uncertainty. We assume partisanship and ideology need not represent the same construct, although they have become more closely related in recent decades. Formally, consider a two-dimensional space where the first dimension represents ideology and the second represents partisanship; these are defined such that a rightward [leftward] move on the first (ideological) dimension indicates a move toward a more conservative [liberal] ideology, and an upward [downward] move on the second (partisanship) dimension indicates a move toward a more strident Republican [Democrat] partisanship. For simplicity, we assume those with positive [negative] values on the second dimension are Republicans [Democrats] and those with positive [negative] values on the first dimension have “conservative” [“liberal”] ideologies. This space is illustrated in Figure 1.

The ideological space for simulations.
Next, consider the relationship between the two dimensions. If we assume each are distributed standard normal and have correlation ρ, then information about one potentially provides information about the other. Moreover, as the magnitude of ρ increases, and ideology and partisanship become more tightly entwined, then information about one’s partisan label provides more information about one’s likely ideology—and those with partisan labels are likely to be more extreme. Formally speaking, if an arbitrary individual in this space is a Republican, then the expected value on the ideological dimension—where higher values indicate higher levels of conservatism—will be

The ideological space as a function of partisan sorting.
However, increasing the correlation between ideology and partisanship also has the effect of increasing within-party ideological homogeneity; the conditional ideological variance of each party is defined as

Polarization and partisan sorting.
While the previous substantive results might not come as a surprise, the utility of this simulation is that it allows us to show that a mechanism consistent with standard patterns of polarization—partisan sorting—is also (theoretically) associated with greater certainty about the ideologies and identities of key institutional players. Greater certainty about the ideologies of the pivots should allow the executive to better tailor executive orders to avoid Congressional reprisal, and greater certainty about the identities of which members of Congress might be pivotal should allow the executive to better tailor lobbying efforts. As we show later, both types of certainty are associated with higher rates of executive order issuance, even conditional on other standard covariates.
To illustrate how partisan sorting leads to greater certainty (of both aforementioned types), we build upon the framework described thus far. For the remainder of this exercise, assume a legislature with one hundred members and two parties—a left-leaning party and a right-leaning one. We assume the executive—the existence of which is assumed solely to determine the orientations of the veto and filibuster pivots—is a member of the left-leaning party. We also assume the strengths of partisanship and the ideologies of the members are drawn from bivariate standard normal distributions, and the two dimensions are correlated at
Conditional on this setup, we sample
After drawing the ideologies, we sort all 100 ideological draws in increasing order, and note the values of the 34th and 60th largest values (analogous to the veto and filibuster pivots for a left-leaning executive), as well as the “party” medians and the overall chamber median. 15 We repeat this exercise 25,000 times over the range of ρ for each value of k. After this, we calculate the number of draws per simulation within the 95% confidence intervals for each combination of ρ and k. 16 Mean ideologies of the pivots are shown in Figure 4, the 95% confidence interval widths of the estimated ideologies of the pivots (a measure of uncertainty) are shown in Figures 5 and 6, and the numbers of “legislators” within the 95% intervals are shown in Figure 7.

Simulated ideologies of pivots as functions of the correlation between ideology and strength of partisanship.

Simulated 95% confidence interval widths of ideologies of “structural” pivots as functions of the correlation between ideology and strength of partisanship.

Simulated 95% confidence interval widths of ideologies of “partisan” pivots as functions of the correlation between ideology and strength of partisanship.

Simulated number of legislators as possible pivots as functions of the correlation between ideology and strength of partisanship.
Examining Figure 4, it is clear that the simulated ideologies of the pivots are functions of the partisan makeup of the legislature and the correlation between partisanship and ideology. However, the interactive effects are only pronounced for the three “structural” pivots—the veto pivot, the filibuster pivot, and the chamber median. For these pivots, as the size of the majority increases, the ideologies of these pivots become more ideologically extreme in the direction of the majority party’s ideology; more extreme ideologies are also apparent when the correlation between partisanship and ideology increases. These results suggest higher degrees of polarization might lead to more ideologically extreme “structural” pivots, though the effect is somewhat dependent on the majority party’s strength in the legislature.
The results are more straightforward for the “partisan” pivots (the party medians)—for these pivots, the effect of majority size is minimal. Rather, the driver seems to be the correlation between partisanship and ideology; as it increases, the partisan pivots move toward their respective ideological extremes.
However, the expected ideologies of the pivots are only part of the story; indeed, the motivating question for this article was one of uncertainty about pivots, and not their ideologies per se. As such, Figures 5 and 6 show that the 95% confidence intervals for the pivots (proxies for the ideological uncertainty thereof) are affected by changes in ρ and majority party size. Figure 5 focuses on the “structural” pivots and shows the 95% confidence intervals about the pivots narrow with increases in ρ, suggesting that political actors might become more certain about the ideological preferences of the “structural” pivots with greater levels of partisan sorting.
Also notable is that the effect of majority size is not monotonic, as it appeared to be in Figure 4. Instead, the narrowest confidence intervals seem to be when the right-leaning party’s size just barely contains (or barely misses) a pivot. For example, the 34th most right-leaning legislator is the veto pivot for left-leaning executives, and the confidence interval for this pivot is narrowest when the left-leaning party commands only about one third of the legislature (or, conversely, the right-leaning party commands about two thirds of the legislature). Similar results are found for the 50th most right-leaning legislator (the median) and the 60th most right-leaning legislator (the filibuster pivot). Presumably, these results are due to the pivots in question being near the ideological “gaps” between parties, and this gap only increases as polarization increases, thus resulting in fewer members—and fewer opposite-party members in particular—near the pivot in question.
Similar, albeit weaker, results are found when we examine the party medians, which are presented in Figure 6. For these pivots, the major determinant of variance appears to be the size of the majority in the legislature, but there is a slight effect for the correlation between partisanship and ideology, with narrower confidence intervals (and therefore less uncertainty about the ideological locations of the pivots) when the correlation is high.
Finally, we examine how changes in the correlation between partisanship and ideology affect uncertainty about the identities of the pivots. This is done by calculating the number of draws per simulation that lie within the 95% confidence intervals for each combination of ρ and k. Substantively, this can be interpreted as the number of individuals who could potentially be the pivot in question. As can be seen, the results in Figure 7 mimic those presented in Figures 5 and 6, as the identities of these pivots become clearer as the correlation between partisanship and ideology increases, and the relationship for the “partisan” pivots is minimal, if it exists at all.
These simulated relationships give credence to our uncertainty concept and suggest that a polarization process consistent with partisan sorting might have theoretical consequences for scholars of institutions. As polarization and sorting increase in a simulated legislature, the certainty around the pivots increases. If the executive has greater certainty about the identities or positions of pivotal legislators, then she may be better able to structure executive orders to preempt Congressional opposition, with the result being that more certainty may lead to more executive orders. Our goal is to test this relationship empirically by examining whether uncertainty over the locations of pivots affects executive order issuance patterns.
An Empirical Analysis of Uncertainty and Executive Orders
As mentioned, prior literature on political institutions (especially within the realm of American politics) has tended to treat the ideological positions of key pivots as fixed (Howell, 2003). However, Cameron’s (2000) model of veto bargaining, which models veto overrides (and failures to override) as a function of the uncertainty surrounding the location of the veto pivot, is an exception. Indeed, Cameron (2000) argues that “uncertainty about the location of the veto override player advantages the president, relative to a world without uncertainty . . . [because] when there is uncertainty about the override player, override attempts will sometimes fail” (p. 105). 17 That is, uncertainty about the location of the veto pivot makes it harder for the legislature to write veto-proof legislation in anticipation of a presidential veto. Greater certainty about the location of the veto pivot, however, should make it easier to write such legislation, thus providing Congress with more of an advantage relative to the president and ensuring that successful overrides occur more often.
However, greater certainty need not advantage the legislature in all battles with the executive. Indeed, while not explicitly predicted by any standard models of the executive order process (in part because pivot uncertainty has not been explicitly incorporated), the same logic underlying Cameron’s (2000) veto model might make executive orders more attractive to the president as uncertainty about the location of key pivots decreases.18,19 Indeed, if presidents know more about the location of the key players, when the legislature will be able to coordinate and fight an executive order, as well as the personal identities of the key actors (and therefore whom to lobby), the president should be able to more carefully tailor his or her executive orders in order to ensure they remain law and placate the requisite influential individuals. 20 Moreover, this certainty is in addition to any accretion of executive power caused by a widening of the gridlock interval due to polarization. 21 Given this additional certainty, an executive should be more willing to issue more policy-relevant executive orders, since he or she will be better able to tailor them to the legislature’s ideological proclivities. Our hypothesis is, therefore, derived:
Executive Order Issuances: Data
To test our hypothesis, we use as our dependent variable the number of Policy-Relevant Executive Orders per Congress, which is drawn from Warber (2006). This dataset includes information on nearly every executive order issued by Presidents Franklin D. Roosevelt through George W. Bush, though to be consistent with much previous work on executive orders, we focus on the timeframe beginning in 1945 (which corresponds to the 79th-110th Congresses). 22
Key to our analysis is that Warber codes all executive orders as belonging to at least one of three different categories—Routine, Symbolic, and Policy-Relevant. Routine orders are those that “do not drastically depart from existing or newly created policies enacted by Congress. Instead, these orders execute responsibilities that are within the legal or perceived scope of Presidential authority” (Warber, 2006, p. 141). Symbolic orders are those that are ceremonial in nature. Neither of these categories reflect major unilateral policy directives; those that do are instead categorized as Policy-Relevant. As Warber (2006) notes, these executive orders “either [depart] from the status quo of a specific policy that has already been implemented, or [interpret] and [implement] legislation that diverts from the original intent of Congress” (p. 143). It is around these executive orders that the ideological and partisan battle lines should be drawn.23,24
Testing our hypothesis requires estimating the uncertainty inherent in the identities of the key pivots as well as their ideological locations. To do this, we implement the following procedure, which is similar to the one employed by Martin (2012):
For each Congress under analysis, simulate 10,000 draws from a truncated normal distribution (bounded between −1 and 1) where the mean vector consists of that Congress members’ “Common Space” DW-NOMINATE (Poole, 1998) scores (hereafter simply referred to as Common Space scores), and the diagonal of the covariance matrix consists of the parametric bootstrapped standard errors of the same (Carroll, Lewis, Lo, Poole, & Rosenthal, 2009). 25
For each simulation and chamber, sort the members’ ideal points.
Extract the chamber-specific veto pivots, medians, majority party medians, and minority party medians, as well as the filibuster pivot from the Senate simulations.
For each Congress, calculate the proportion of legislators who were any of these key pivots in at least one simulation. 26
For each pivot–Congress combination, calculate the difference between the maximum and minimum Common Space scores by those who were the veto pivot at least once, creating a range of ideologies for each pivot–Congress combination. We then take the mean of these pivot–Congress interval widths to create a single value for each Congress.
Repeat for each Congress.
The aforementioned process generates our key covariates for each Congress, a Proportion version of Pivot Uncertainty (calculated in Step 4), and an Interval Width version (Step 5). We use two measures because they capture different concepts—the Proportion version captures uncertainty regarding the identity of the key pivots, and the Interval Width version captures uncertainty regarding the ideology of the key pivots. Indeed, as Clinton, Jackman, and Rivers (2004) note, these are distinct, as “relatively precise knowledge of where the pivots lie does not [necessarily] correspond to knowing the identity of pivotal legislators, whose votes are necessary to guarantee cloture or veto-proof majorities” (p. 361) though these concepts are likely correlated. Nonetheless, the two concepts likely differ from the perspective of the president and other key actors—knowing the ideology of the key pivots likely provides broad knowledge regarding the contours of a bill or executive order and what is likely to pass, and knowing the identities of key pivots likely provides specific information regarding who to lobby in order to ensure bill passage (or prevention of a veto override, in the present case).
Thus, our measures are based on the individual level uncertainty for each member because they are generated from the standard errors of the ideal point estimates. The Proportion measure, which captures uncertainty about the exact identity of the pivot, is useful in that it captures the president’s ability to engage in direct lobbying efforts with one or a small group of individual legislators. For example, the executive may offer a particularized benefit to an individual legislator when the Proportion Uncertainty is low, which allows the executive more information about the identity of the pivot. In slight contrast, the Interval Width measure instead captures information about the ideology of the pivot, rather than their exact identity. This information may be useful to the executive because it may allow him or her to alter the content of the executive order to appease the possible ideological positions of the pivots. This ideological adjustment of the executive order can be more effective if the executive has more precise information regarding the exact ideological position of the pivot, which is facilitated by increased certainty.
To these uncertainty measures, we add several other variables that previous studies of executive orders have shown to be important. To capture institutional (pivotal) concerns, we include the Distance Between Chamber Median and the Filibuster Pivot as well as the Distance Between Chamber Median and the Veto Pivot, both of which should be positively related to the number of policy-relevant executive orders, due to their implications for legislative inability to act. 27 To account for the fact that more institutionally capable legislatures will be better able to oppose executive orders (Bolton & Thrower, 2015), we include Legislative Expenditures, defined as logged legislative expenditures in billions of 2009 dollars, which proxies for the size and capacity of Congress as an institution. 28 As we posit that Pivot Uncertainty is a result of lower levels of partisan polarization, we include Interparty Divergence (measured as the Congress-level difference between the party medians, pooling across both chambers) and Intraparty Divergence (measured as the Congress-level arithmetic mean between the party-specific standard deviations of Common Space scores; that is, for each Congress, we separately calculate the standard deviations of each party’s Common Space scores and take the mean of the two in order to calculate Intraparty Divergence) as well, to account for possible other effects of polarization and also to ensure that our Uncertainty measures are not simply picking up the effects of Interparty or Intraparty Divergence due to correlation between the two; that is, these variables are included to ensure that the specific mechanism of ideological uncertainty is of relevance.29,30 In addition, to capture other partisan concerns, we include Unified Government (which equals one if both legislative chambers and the executive branch are controlled by the same party, and zero otherwise). We also include First-Term President of Different Party, which equals one if the current president is in his first four years and of a different party than his predecessor, and zero otherwise. This captures the notion that these presidents might have (or at least perceive themselves as having) mandates to enact policy change, which could lead to more deference by Congress. 31
Executive Order Issuances: Method and Results
Before proceeding to the empirical models, we first check to see whether the theoretical expectations regarding the relationships between Interparty and Intraparty Divergence and our Pivot Uncertainty measures are borne out in the data. Figure 8 plots the relationships, along with a linear regression line and the 90% and 95% confidence intervals. As can be seen, the relationship is present for both uncertainty and both polarization measures, with negative [positive] correlations between Interparty Divergence [Intraparty Divergence] and both Pivot Uncertainty measures. As expected, greater cross-party divergence and greater intraparty homogeneity (less intraparty divergence) are both associated with higher levels of certainty regarding the identity and ideology of pivots. These relationships hold regardless of which Pivot Uncertainty measure is used, though they are stronger for the Interval Width measure; this should not come as a surprise, since the Interval Width measure is probably a better approximation of the ideology of the key pivot, where the Proportion version of the measure is a better approximation of identities thereof.

Inter- and intraparty ideological divergence and pivot uncertainty.
Turning to our main empirics, we estimate a series of negative binomial regression models. Since we have so few observations (N = 32), we estimate a series of models with various combinations of the covariates of interest. Results are presented in Table 1.
Negative Binomial Models of the Determinants of Policy-Relevant Executive Orders.
Note. Standard errors in parentheses. AIC = Akaike information criterion.
Two-tailed tests: *p < .1. **p < .05. ***p < .01.
As can be seen, the results support our hypothesis, although we find stronger results when the Proportion version of the Pivot Uncertainty measure is used. In all models where it is present, our Proportion measure is negative and significant, indicating that uncertainty over the identities of the key legislative actors is associated with the issuance of fewer policy-relevant executive orders. In addition, the Interval Width version is also negative and significant in most models where it is present, indicating that uncertainty over the ideological locations of key institutional constraints is also associated with fewer policy-relevant executive orders. Moreover, the effects are substantively significant, as evidenced by Figure 9, which presents predicted counts of policy-relevant executive orders as a function of both kinds of Pivot Uncertainty; a shift in Pivot Uncertainty from two standard deviations below its mean to two above decreases the expected number of policy-relevant executive orders from about 99 to about 31 for the Proportion measure, and from about 66 to about 38 for Interval Width. 32

Pivot uncertainty and executive order issuance.
Taken together, the results for our Pivot Uncertainty measures suggest that uncertainty is particularly important for the executive’s role in anticipating legislative responses to executive orders. Our results are consistent with the idea that the executive takes into account both the possible ideologies of the key legislative players, as well as the identities thereof, and adjusts her behavior accordingly. 33
The Independent Relevance of Uncertainty
Importantly, the empirical and theoretical relevance of our Pivot Uncertainty measures extends beyond the regression results discussed in the previous section. In an attempt to determine whether our Pivot Uncertainty measures explain executive order issuance patterns better than more conventional measures of partisan and institutional constraints, as well as whether they explain variation above and beyond that explained by more conventional variables, we perform a series of model tests. First, we perform a series of likelihood ratio tests to determine whether adding Pivot Uncertainty to our other covariates of interest (and, conversely, whether adding the other covariates to models solely containing Pivot Uncertainty) significantly increases model fit. That is, we examine whether Models 2 to 8 and 10 to 16 in Table 1 fit the data better than analogous models without our Pivot Uncertainty measures. We then examine whether Models 2 to 8 and 10 to 16 fit the data better than Models 1 and 9 (respectively). Significant test statistics indicate that the model with the additional covariate(s) provides a better fit than the relevant comparison model without the additional covariates, thus suggesting that the added covariates provide additional explanatory power. Results are in Table 2.
Nested Model Tests.
Note. The entries in each cell indicate the likelihood ratio test statistic of the encompassing model created by the addition of the listed variables to the listed “baseline” model versus the listed “baseline” model without the additional covariates. Statistical significance indicates that the listed covariates improve model fit.
Two-tailed tests: *p < .1. **p < .05. ***p < .01.
The results in Table 2 provide further evidence for the importance of uncertainty. In all seven cases where it is examined, adding the Proportion version of the measure to those models without it increases model fit, suggesting that additional information about who is likely to be a key player has strong effects on the outcomes of interest. Conversely, adding the Interval Width versions of our Pivot Uncertainty variable to models without it increases model fit in only four of the seven models. In addition, adding other covariates to a model where Pivot Uncertainty is the only covariate increases model fit to a significant degree in only one of the seven cases where the Proportion measure is used, as opposed to three of the seven cases with Interval Width. Collectively, these results suggest that not only is uncertainty important, but it may—depending on the type of uncertainty under analysis—even be more important than other theoretically informed explanators of executive action.
Nonetheless, these tests are useful and consistently find support for the importance of uncertainty. However, it should be noted that Clarke (2001) warns against using encompassing models to test competing theories against one another, as this approach does not discriminate between models per se (in the present case, this approach only determines whether our Pivot Uncertainty measures have explanatory power above and beyond that of the other covariates of interest, as opposed to instead of the other covariates). Indeed, this approach “discriminates between [a model of interest] and a hybrid model that is neither [model of interest]” (p. 731). As such, Clarke (2001) instead advocates for the use of nonnested model tests. One of the most commonly used such tests in political science is Clarke’s (2007) distribution-free test. This test is based on the Kullback and Leibler (1951) distance, which can be thought of in the present case as a statistical measure of “closeness” between the estimated models and the “true” model. In practice, under the distribution-free test, two models will be considered to be statistically equivalent if the log-likelihood ratios of the observations are evenly distributed about zero; deviations from this distribution, with more than half of the ratios being greater than zero (indicating more observations whose log-likelihoods under one model are consistently higher than the analogous log-likelihoods under the other) will suggest one model is preferred to the other. We use this test to compare those models with covariates besides our Uncertainty measures to ones where the Uncertainty measure is the only covariate. Results are in Table 3.
Nonnested Model Tests.
Note. The bolded entries in each cell indicate which model fits better according to the Clarke test, and the test statistics—the proportion of cases for which the listed (bolded) model produced individual log-likelihoods higher than that of the comparison model—are listed below the model. Statistical significance indicates that the listed covariates improve model fit.
Two-tailed tests: *p < .1. **p < .05. ***p < .01.
Impressively, the Clarke (2007) tests choose the uncertainty-based models over the others in all cases when the Proportion version of the measure is used, with the test statistic significant in all cases. However, the results are not as strong when the Interval Width version of the measure is used; in these cases, while the Clarke test chooses the Interval Width model in all cases, the test statistic is significant in only five of the seven cases.
These results provide further support to the results presented in Tables 1 and 2 in that uncertainty is important to understanding patterns of executive order issuance, and may even be more important than standard covariates. However, they—along with our previous results—also suggest that the theoretical dynamics underlying our different measures of uncertainty are conceptually distinct. The Proportion version of the measure, which taps into latent uncertainty over knowing who the key pivots are, tends to perform better in nested and nonnested model tests, and also has stronger substantive effects on the dependent variable of interest (as seen in Figure 9).
Conversely, the Interval Width version of the Pivot Uncertainty measure, which taps into uncertainty over knowing where in ideological space the key pivots are, performs worse in nested and nonnested model tests, and has somewhat weaker substantive effects. Collectively, the results not only suggest that uncertainty plays an important role but also suggests that a particular kind of uncertainty—that is, uncertainty over who the most influential legislators are—is key.
Discussion and Conclusion
Much recent research into the positions and interactions of institutional actors has focused on the role of ideological and/or partisan conflict, which is often approximated by the ideological divergence between relevant party actors and/or other theoretically driven institutional constraints, unified/divided government status, partisan compositions in some branch of government, and the like. Polarization, resulting in part from higher levels of partisan sorting, will affect the observed values of some of these variables, commonly manifesting as higher levels of ideological divergence between parties, the disappearance of more moderate political actors (at least at the elite level), and higher partisan stakes for myriad political decisions.
Here, we focus on another, understudied, effect of polarization—an increase in intraparty ideological homogeneity, which leads to less uncertainty about the ideological positions of key institutional actors, as well as less uncertainty about the identities of the same. Put differently, higher levels of polarization will provide greater clarity about the ranges of possible policies that might survive override attempts (as in the case of executive orders) and will also provide greater clarity about the identities of those key legislators, which itself has implications for lobbying and policymaking strategies (Clinton et al., 2004).
Incorporating measures of uncertainty into empirical models of the executive order process reveals interesting results, the implications of which go far beyond the immediate empirical applications. Indeed, we find that greater certainty about the identities of key institutional actors is associated with the issuance of more policy-relevant executive orders. Strikingly, this measure often outperforms other explanators, which we confirm via both nested and nonnested model tests. Weaker, but substantively similar, results are found when we include in our models a measure that captures the uncertainty about the ideological locations of key institutional actors; greater certainty tends to be associated with more executive orders, though the comparative strength of this measure versus extant ones is somewhat weaker.
These results have important implications for the study of the Presidency, in that they suggest the office’s power might be modulated not only by the ideological divergence that results from polarization (as mentioned, the ideological divergence between the two parties was also a significant predictor of executive order issuance whenever it was included in our empirical models) but also by informational advantages that result from increased levels of polarization-induced intraparty ideological homogeneity. This suggests other interactions with Congress—such as veto bargaining (Cameron, 2000; Cameron & McCarty, 2004; Groseclose & McCarty, 2001; Martin, 2012) and appointments (Hollibaugh, Horton, & Lewis, 2014; Lewis, 2008, 2011; Sen & Spaniel, 2017)—as well as interactions with the courts—such as the extent to which presidents can use their legal discretion when setting policy unilaterally—might be similarly affected by what might be the president’s polarization-induced informational advantages. In addition, our results might be able to provide leverage on the distinction between more “unilateral” models of executive orders where the president is able to use executive orders to perform end-runs around recalcitrant Congresses, and more “conditional” models wherein the president needs tacit approval from at least one key member of Congress (Chiou & Rothenberg, 2014, 2017; Deering & Maltzman, 1999; Fine & Warber, 2012; Howell, 2003; Krause & Cohen, 1997; Mayer, 2002); indeed, the distinction may simply be that presidents seemingly act more “unilateral” when they have greater information about key members of Congress, and are seemingly more constrained by Congress when they are at an informational disadvantage. Relatedly, informational advantages in the realm of foreign policy might help explain why presidents are seemingly more unconstrained when issuing foreign-policy-related executive orders (Marshall & Pacelle, 2005).
Moreover, our results have implications for the study of polarization as well as models of institutions. For the former, they suggest that scholars should seriously consider both interparty ideological divergence as well as intraparty ideological homogeneity when studying the effects of polarization. To date, most research has focused on the former, and the results here suggest that the latter should also be considered. In addition, the results here suggest it might be worthwhile to further refine formal models of institutions to incorporate uncertainty about the personal identities/ideological locations of the key actors. Doing so would enhance the theoretical richness therein and may point future scholars in new directions about the theoretical relevance of polarization and institutions. Indeed, other scholars have considered in passing the possible theoretical relevance of uncertainty, but aside from Cameron’s (2000) model of veto bargaining, efforts to formally and/or empirically incorporate it have been minimal. 34 Moreover, future research should also examine whether polarization always increases the first-mover advantage—as it does here—or whether the effects are more conditional on institutional arrangements. These dynamics may also be important for uncertainty between legislators, especially as it relates to Cameron’s (2000) framework. If legislators have more certainty about the positions of other legislators, it may aid in veto override efforts, impeachment proceedings, or other Congressional actions that require coordinated efforts.
In addition, it might be worthwhile to extend this study to the state level. There is a great deal of variation in institutional structure and veto power across the fifty states, such as the line-item veto and different veto override thresholds, and this would allow us to better pin down the mechanisms underlying the relationship between polarization and executive power. In this vein, Shor and McCarty’s (2011) cross-state ideological estimates would allow us to pool across states for additional statistical power, and different trends in state-level polarization would allow us to better unpack the effects of polarization versus other time-varying covariates on ideological uncertainty.
In sum, without also addressing the empirical and/or substantive uncertainty underlying these estimates, scholars may be misled about inferences drawn from models that focus solely on the ideological locations of key actors. And fully understanding the effects of polarization on institutional politics might be the key to fully grasping the causes—and consequences—of contemporary political dysfunction.
Supplemental Material
Appendix – Supplemental material for The Effects of Polarization on Ideological Certainty: An Application to Executive Order Issuance
Supplemental material, Appendix for The Effects of Polarization on Ideological Certainty: An Application to Executive Order Issuance by Mark Brockway and Gary E. Hollibaugh in American Politics Research
Footnotes
Acknowledgements
We thank Keith Poole and Adam Warber for data. All errors remain our own.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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