Toward a theory of minority-party influence in the U.S. Congress: whip counts, amendment votes, and minority leverage in the house

Abstract The literature on congressional decision-making has largely ignored the influence of the minority party in the legislative process. This follows from the widely held belief that the majority party dominates the agenda-setting process. Though the minority party rarely achieves major policy success in Congress, we argue that the minority has significantly more influence over the legislative agenda than is commonly believed. We posit that, under some conditions, the minority has enough bargaining leverage to get floor votes on their proposals, in the form of both amendments and bills. We test our theoretical expectations with a novel design utilizing whip count data from the House and show that when a whip count on a bill occurs, the likelihood of a minority amendment disappointment and a majority amendment roll increases, respectively. This suggests that the more leverage the minority party has, the more we see their legislative proposals on the floor.

party power in Congress; the minority party, by comparison, has no theoretical role in governing. 1As a result, scholars' conception of party power in Congress is in keeping with the quote by Thomas Reed abovethe majority party rules, while the minority party is left to sit and watch (and perhaps complain).
Yet to many political observers, this characterization is unsatisfying.While there is overwhelming evidence that the majority party possesses a significant legislative advantage, it seems unlikely that its advantage is absolute.Rather, the minority party likely plays some role, at least under some conditions, which renders the outcome of the process different than it would have been in their absence.
Consider, for example, H.R. 2210 -The School Readiness Act of 2003introduced by Rep. Michael Castle (R-DE) in the Republican-controlled 108th Congress.The legislation sought to amend the Head Start Act of 1981which provided comprehensive developmental services, including health, nutritional, educational, social, and other services, to economically disadvantaged preschool children and their familiesby reauthorizing some programs, removing nondiscrimination requirements for religious institutions receiving funds, and allowing eight states to receive block grants to coordinate the establishment of childhood education programs with the Secretary of Education.Democratic leaders announced their opposition to the measure immediately after its introduction (Swindell 2003), forcing Republican leadership to keep their relatively slim margin intact.The fate of the bill was made more uncertain when a group of fiscal conservatives threatened to vote against it (Swindell and Schuler 2003).With the defection of these vital votes, the GOP leadership needed to find some other way to ensure a majority.
A clue as to how the Republicans accomplished this lies in the form that the floor debate took.The measure was considered under a structured rule (H.Res.336), which permitted the consideration of two minority amendments.The first (H.Amdt.321), offered by Rep. Lynn Woolsey (D-CA), aimed to remove the provisions providing for the exemption of religious institutions from nondiscrimination requirements.It failed 199-231, with 4 Republicans voting for and 7 Democrats voting against.The second (H.Amdt.322), offered by Rep. George Miller (D-CA), sought to remove the block grant program from the bill and similarly failed on party lines (200-229) with 4 Republicans voting for and 7 Democrats voting against.These amendments are peculiar if party power lies solely with the majority; in such a framework, what motive would GOP leadership have in forcing their members to take public positions on the two most controversial parts of the bill?
The final vote on H.R. 2210 provides some insight here.Even after bringing in Rep. John Sullivan (R-OK)recently injured in a car crash and under orders for bed reston a wheelchair and swaying Reps.James Leach (R-IA) and Steven LaTourette (R-OH), who had waited until the last minute to be sure their votes would be decisive, Republican leadership only mustered 217 votes with no Democrats for and 12 Republicans against.The measure passed by a bare majority, 217-216, because two Democrats abstained from voting.2 1 To be fair, Rohde (1991) does devote a chapter to the minority party, but it does not play a significant conceptual role in his understanding of partisan governance.
In light of examples like this, we argue that the minority party's ability to make proposals on the House floor is not as rare as has been assumed.Yet, the extant literature does not offer a clear, unified way to think about this theoretically. 3While we largely agree with contemporary theories of party power in Congressthat the majority party dominates the agenda processwe also suspect that incorporating the role of the minority party will be an important next step in explaining a substantial part of what happens in the U.S. House.While we have some sense of what it means for outcomes if the minority can make these type of proposalsnamely, that systematically considering minority-party proposals on the floor should have a moderating effect on final outcomes (Krehbiel et al. 2015) we have little sense how, why, and when the majority leaves the door open for minority proposals.
In this paper, we begin to fill this gap by conceiving of ways that the minority party might be able to wield some influence in the House and consider what they might seek to achieve as a result.To do this, we first take some initial steps toward building a theory of minority-party influence in Congress.We assume that, at least in some instances, the minority party's ability to withhold marginal voteseither those necessary for passage or that allow majority party moderates to defect to satisfy their constituencygives them enough leverage to realize some policy or electoral gains by forcing votes on policies that they care about or that the majority finds difficult in front of their constituents.
We then build a theory of measurement for our central concept of leverage.In doing so, we first examine two indicators: (1) minority disappointment rates (how often a majority of the minority party supports a bill/amendment that ultimately goes down to defeat) and (2) majority roll rates (how often a majority of the minority party supports a bill/amendment that passes over the objections of a majority of the majority party). 4A close look at these data suggests that the amendment stage is where most of the minority party's leverage is realized; this informs our operationalization strategy in which we look at all amendment votes that accompany a bill.Indeed, in focusing on amendments, we help to address a shortcoming in a congressional literature that perpetually over focused on finalpassage outcomes on bills. 5inally, we test our hypothesisthat greater minority leverage leads to more minority proposals on the floorusing majority-party whip count data.That is, we assume that House bills that are whipped by the majority are in the minority leverage condition, such that we expect these bills to give the minority the best opportunity to extract agenda concessions from the majority by threatening to withhold marginal votes.In a series of regressions, we find that majority whip counts are positively associated with both minority amendment disappointments and majority amendment rolls in the House, and these results are robust to the inclusion of a variety of covariates.

3
In this lamentation, we follow in the line of Jones (1970), who set out to understand the differences between the minority and majority parties.
The role of the minority party in the existing theoretical literature As noted, the dominant partisan theories (cartel and CPG) of congressional decision-making are structured entirely around the majority party.In cartel theory, it is assumed that the agenda process is dictated by a small group of majority-party leaders who act on behalf of a majority of the caucus (represented by the ideal point of the median party member) (Cox and McCubbins 1993, 2005).Here, the heart of party power comes by installing multiple veto points in the agenda process, so that the majority of the majority party is never "rolled" on the floor (i.e. a majority of the majority never opposes a bill that subsequently goes on to pass).In CPG theory, when the parties are internally homogenous and distinct (polarized) from one another, members of the majority party delegate power to their leaders to structure the agenda such that policy initiatives that a majority of the majority support are pursued (Rohde 1991; Aldrich 1995; Aldrich and Rohde 2001).While cartel theory is about the majority party seeking to avoid harm and CPG theory is about the majority aggressively seeking to pass new policy (when the "condition" is satisfied), both are majority party-centric; neither affords the minority a meaningful role in the agenda process.
The other dominant theoretical approach is distinctly non-partisan, in that congressional decision-making is driven entirely by majoritarian or supermajoritarian voting rules and the aggregation of legislator preferences through these procedures.In these treatments, pivotal actorsthe floor median in the House (Krehbiel 1991), and the filibuster and veto override "pivots" in a more general inter-branch formulation (Krehbiel 1998)make important decisions, and parties are treated as epiphenomenal.When parties are considered in more depth, their exclusion stems from a belief that the majority and minority parties cancel each other out; that is, neither party organization possesses disproportionate agenda power.In effect, the minority is ignored just like in the party cartel and CPG theoriesbut the majority is ignored as well. 6ore recently, several accounts have emerged to more fully appreciate the minority party's role in Congress.Gailmard and Jenkins (2008), Green (2015), and Egar (2016) look at a range of voting and extra-legislative data that suggest an underappreciated role for the minority party. 7 Ballard and Curry (2021) argue that the confluence of three factorsconstraints on the majority party, minority party cohesion on the issue at hand, and the minority party's motivation to engage in legislating rather than electioneeringinfluences minority party capacity on finalpassage votes.Krehbiel et al. (2015) offer a formal theory of partisan lawmaking, wherein both majority and minority parties are able to offer amendments and use transferable resources to assemble winning or blocking coalitions, which lead to more moderate policy outcomes.Thus, after decades of neglect, there is now a growing literature that takes seriously minority-party influence in the House over legislative outcomes.Left unanswered by these recent accounts, however, is a systematic understanding of how, why, and when the majority ever lets the minority party have access to the agenda to offer amendments.In order to address these questionsand take the next step forward in theoretically understanding minority-party influence in Congresswe need to further elucidate the conditions under which the majority might allow the minority to play a role in the policy-making process.

Minority influence in Congress: theoretical foundations
With these prior investigations in mind, we construct a theory to explain minority party agenda access in the House.To do this, we first need to establish the source of the minority's leverage and then consider what they will seek to achieve with that leverage.We take these topics in turn, outlining major assumptions and connecting with a logical framework that yields our key hypothesis.

The source of minority-party leverage
Before examining the source of minority-party agenda access, it is useful to clearly define what we mean by "leverage" and, relatedly, what we mean by "influence."By leverage, we mean bargaining powersomething of value that can be traded for something desired.Influence, as we use it, is then the spoils from this bargaining power.That is, where we use influence here, we use it as a noun, not a verb.We see influence over legislative behavior and outcomes as a produce of minority-party leverage.
We argue that the fundamental source of the minority party's leverage in the modern House is tied to its ability to supply marginal votes.This assumption follows straightforwardly from the observation that, even with a majority of seats in the chamber, some of the majority party's legislative priorities will find serious opposition from its moderate members. 8Often, even widely popular planks in the party platform will run afoul of constituencies in marginal districts, where majorityparty members will be absolutely unwillingfor fear of their electoral lifeto cast a vote in favor of the policy (King and Zeckhauser 2003). 9In such cases, a hand full of "yea" votes from minority-party members will be pivotal in passing these party priorities to create the potential for new law.The same is true even when moderate opposition is extant but not as rigid.Although passage could be secured with only majority votes through some mix of carrots and sticks, carrots are a scarce resource 8 Here, one might object that this assumption seems to rest heavily on the implicit notions that bipartisanship is mostly absent in the House and politics in that chamber are mostly unidimensional.We agree that these assumptions simplify the reality of the chamber.Yet, we hasten to point out that the more bipartisanship and multidimensionality dominate the patterns of behavior in the House, the less likely we are to find support for our theory.Thus, in a sense, we prefer to let the data tell us whether those are assumption that are crucial for us to modify.and spending valuable time whipping moderates is costly (Evans 2018).Indeed, even if carrotssuch as desirable committee seats, earmarks, or campaign fundswere plentiful, Mayhew's (1974) thought experiment reminds us of the proximity of reelection concerns.That is, if certain votes are hard for moderates to explain away at election time, then no amount of other side-payments is likely to get them on board. 10Thus, we assume that soliciting minority votes can be a cost-effective strategy.And sometimes it is the only strategy. 11ritically, this assumption implies that minority votesand thus minority leveragewill be valuable on some bills but not all or even most bills.This feature is different than (and complements) the approach taken in Ballard and Curry (2021), which considers every bill and joint resolution in the House, and fits nicely with the canonical view that the minority, much of the time, simply stands by and watches the process.Yet where minority-party leaders can credibly threaten to prevent their moderate members from supporting majority-party proposals, they can generate leverage to bargain with the majority over access to the agenda.12

Achieving minority-party goals
Our second argument is that the minority party uses its leverage in pursuit of concrete goals.The core of this argument relies on the assumption that the minority party's first goal is to change and/or pass policy.For House members, the benefits of achieving those policy goals are both a means of fulfilling their representational contract with their constituents (including the special interests that help to fund their campaigns for election and reelection) and an end in and of themselves, inasmuch as legislators have personal policy-driven motives for seeking office in the first place.
Given the institutional barriers that make policy change costly for the minority party, it is difficult for them to pass significant legislation without a majority of House seats.The best way to achieve policy change in the House is to hold power, and thus the minority party aspires to become the majority party; in a sense we might view this as a purely electoral goal.In order to recapture the majority, the minority must persuade enough voters in enough critical districts to replace majority-party members with their members.Recapturing the majority simply for the sake of doing so is a not a particularly useful way to think about this goal, however.We instead argue that it is more useful to envision the minority party's 10 One interesting scenario that we do not theorize about here involves the extreme wing of the party -The Freedom Caucus for the Republicans or House Progressive Caucus for the Democrats, for exampledefecting on a majority party initiative.Certainly, this can happen, and extra minority-party votes are helpful in this scenario as well.It is less clear to us, however, whether the majority party wishes to "release" these members for electoral reasons, since it seems unlikely that members from the extreme wings of the party are likely to lose their seats to the opposite party (even if they might be defeated in the primary).
11 Implicitly, we are assuming a repeat play context, where the costs for the minority of reneging on promise to provide votes on a majority party proposal after their floor amendments for that bill are complete outweigh the benefits of doing so.
desire to achieve majority status as a desire to obtain a less expensive avenue for producing policy change in future Congresses. 13hat is, the "cost" of changing policy as the minority party is likely to be quite expensive on a per item basis, relative to changing policy as the majority party.Thus, the choice to invest in recapturing majority status is also an investment, of sorts, in cheaper policy change. 14This calculation becomes clearer if considered in dynamic terms.Envision a minority party, at the beginning of a given Congress, whose policy aspirations span a number of Congresses into the future.The minority's decision to invest resources in effectuating immediate policy change (during the current Congress) versus investing those resources in trying to increase their probability of achieving majority status in a future Congress hinges on (1) the relative cost differential in changing policy as the minority party versus the majority party and (2) how much they can increase their probability of recapturing majority status.
To see how these factors interact imagine a hypothetical world that is three Congresses long.In this world, the minority party can pursue two different strategies.The minority can spend the first two Congresses forcing numerous votes on things that will never change policy in their preferred direction but will set them apart from the majority electorallyeffectively attacking/exposing vulnerabilities in the majority's electoral prospectswith the hope of becoming the new majority party in the third Congress.Alternatively, the minority can work toward changing a few policies in each of the three Congresses but never achieve enough to significantly increase their probability of recapturing the majority. 15How do these two strategies compare?
For simplicity, assume that the latter strategy yielded precisely three major policy changes for the minority per Congress, for a total of nine minority policy goals achieved over our hypothetical three-Congress period.The essential question then becomeshow many policy changes the party could achieve in one Congress as the majority, if they successfully pursue the former strategy and regain majority control in the third Congress.In our example, where the minority can change three policies per Congress, if the majority party can achieve more than nine policy changes in one Congress, then the latter strategy is preferred.Put in slightly more general terms, if the minority party could gain greater total policy influence in a future session where they hold the majority as compared to the minor concessions it could receive while in the minority then that party should invest their resources and leverage toward recapturing majority status, even when policy change is the primary goal.
Our observation of congressional policymaking leads us to assume that the discrepancy between the number of policy goals that can be achieved as the minority 13 Various other benefits also follow from majority status.Most notably, members have an easier time raising campaign dollars (Cox and Magar 1999; Cann 2008) and get a larger share of the particularistic projects allocated by Congress (Crespin and Finocchiaro 2008).However, we argue that the major policy benefit of majority status outweighs and overshadows these secondary benefits.
14 An additional reason that the minority might prefer to invest in a patient strategy for policy change is the logic of Schwartz's (2021) parties as "long coalitions."Here, parties are conceptualized as representing bundles of interests that expect long-term representation, rather than short-term policy changes.and the number of policy goals that can be achieved as the majority is very large.Therefore, if the recapture strategy has even a modest impact on the likelihood of achieving majority status, then the minority party is highly likely to invest in it.If so, then we should observe the minority forcing many votes on floor proposals in the form of amendments or bills but with relatively little success at changing policy.From this logic, we derive the following: Hypothesis: The minority party will be more likely to have its proposals considered on the floor as their leverage increases.
At first look, one might be inclined to see this prediction as somewhat tautological; that is, one might assume that leverage would automatically translate into access.Instead, however, we assume that the minority party might use its leverage for a range of things, such as increased shares of distributive benefits or other non-policy concessions such as staff or office space (Cox and McCubbins 2005, 46).
Notice that we are broad in identifying "proposals" that the minority party will seek to get on the agenda.That is, based on the logic of the last assumption, they should be perfectly happy to schedule votes on proposals that will lose, and on proposals that come up only as amendments (as opposed to a full bill); the key for the minority is that they are allowed to take positionsand force the majority to take positionsthat will increase their electoral odds of gaining majority status.This is reflected in the next section, where we move on to a systematic test of our hypothesis, using whip count data from the U.S. House to operationalize minority-party leverage to predict patterns of minority-party agenda access at the amendment stage.

Theory of measurement
To reiterate, the key causal concept informing our theory is "leverage."To transform this concept into tractable measures, we first examine two indicators: minorityparty disappointments and majority-party rolls.Minority-party disappointmentswhen a majority of the minority party supports an amendment or bill (on final passage), but it ultimately fails on floorare, by definition, proposals that are opposed by a majority of the majority party.Given that disappointments (1) have the support of half or more of the party but (2) fail to pass, and thus cannot lead to new law, they are perhaps a better indicator of proposals that are broadly intended for position-taking (electoral) benefits but not policy change.Majority-party rolls (when a majority of the minority party supports an amendment or bill on final passage and it passes despite opposition from a majority of the majority party) also effectively separate the party positions but represent potential policy change rather than position-taking, since the bills pass and do raise the possibility of new law.Comparison between minority disappointments and majority rolls will be instructive vis-à-vis minority-party strategyand majority-party responseover time.
We generated majority-roll and minority-disappointment data using the Political Institutions and Public Choice (PIPC) House Roll-Call Database, which spans the 83rd (1953-1954) through 114th (2015-2016) Congresses (Crespin and Rohde 2018).We tallied the number of minority-party disappointments and majority-party rolls on amendment (final-passage) votes, and then divided that number by the total number of roll-call votes on amendment (final-passage) votes for each Congressthis produced minority-party disappointment rates and majority-party roll rates for the House in each Congress.We present these data (in four line graphs) in Fig. 1.
The final-passage-vote data line up closely with the monolithic partisan theoriesthe majority final-passage roll rate and minority final-passage disappointment rate remain at or very near zero for the entire time series (indeed, the modal outcome for the minority final-passage disappointment rate is zero).If we look at the amendment stage, however, the picture is significantly less clear.The minority amendment disappointment rate steadily increases over time from about 10% to over 50% (in the 114th Congress).
These results suggest that the minority is able to leverage votes on amendments that they support and that the minority party is able to influence policy outcomes more often during the amendment process by rolling the majority party, which rarely happens on final-passage votes.Thus, by looking at all of the amendment votes that accompany a bill, 16 we can cast a wider net to capture the leverage that does or does not exist for the minority party on that bill.17Given that almost all amendments in the modern House are offered by permission given in a structured special rule, one might wonder why we do not instead try to model the effect of leverage on the structure of special rules.Our reasoning is two-fold.First, amendments are the actual substance that the minority cares about, not the rule itself; the provisions for amendments in the rules are means to ends.Second, to the extent that there is a relative bias between the structure of rules on bills and the amendments that are actually voted on bills, it is likely to exist such that we are more likely to find null effects using the amendment measure than we would were we to use the special rules measure.
To operationalize leverage given these insights we look for those cases in which the minority can provide or withhold marginal votes to the majority that are likely to be pivotal to the success of a majority party initiative.Our research design uses a majority whip count (i.e.whether a bill received a majority whip count or not) as the indicator of whether the majority party feels vulnerable on an important piece of legislationand, if so, the minority has "high leverage"18 Specifically, whip counts are polls conducted by the Majority Party Whip to gauge how co-partisans plan to vote on a piece of legislation. 19The majority party uses whip counts to give leadership a sense of whether there are enough votes in favor of the majority-party position on a given piece of legislation and to learn how to garner sufficient support (if it is lacking) before a floor vote (Burden and Frisby 2004).The majority does not use whip counts for all pieces of legislation, howeveronly when leaders are uncertain about the outcome.As a result, the number of majority whip counts has fluctuated between eighty and a hundred per Congress over the last 50 years (Evans and Lapinski 2005; Evans 2018).
Whip counts fulfill two distinct and pertinent conditions necessary for operationalizing instances in which the minority party has extra leverage.First, there are items on the agenda that the majority party cares about passing.Second, there must be uncertainty about whether the bills that the majority cares about will pass.Majorityparty leaders would not conduct a whip count if (a) they did not care about the bill passing or (b) they were certain that it would pass.Further, in many instances, majorityparty leaders use whip counts to pressure co-partisans toward positions they prefer due to uncertainty of the outcomes of legislation (Burden and Frisby 2004).
Employing whip counts as an indicator of high minority-party leverage may be critiqued in several ways.First, consider a scenario where the majority party is overly cautious (risk averse) and thus conducts more whip counts.If this is the case, then we expect our whip variable to wash out because the minority party is not using leverage for potential policy gains. 20Alternatively, consider a scenario where the majority party is internally conflicted.For example, during the Conservative Coalition era, Southern and Northern Democrats often had different policy preferences, which caused the party to sometimes be split.In this case, whip counts on a bill may not signal a high leverage situation but rather the minority taking advantage of the majority's lack of cohesion.We believe that even if the minority seizes the opportunity to propose more amendments due to a divided majority party, whip counts still reveal bills where the minority has high leverage.
Another potential critique of this measure is thatbecause we use whip counts on bills rather than amendmentswe lose some of the nuance of the amendment battles in our data.Certainly, we do overlook that nuance; but from a theoretical perspective, we argue that coding these fights at the bill-level is correct because the bill-level fight is where minority-party leverage is drawn from.The contours of the they do not offer the same position taking allure of standard amendment votes.Second, especially for motions to recommit, these are single-shot opportunities, thus limiting amendments to a singular attack.amendment fights are interesting, and deserve greater attention, but they are beyond the scope of our theoretical explanation.

Data and research design
To evaluate our hypothesis, we use House roll-call data discussed above, compiled in the PIPC Database (Crespin and Rohde 2018), and whip-count data from the Congressional Whip Count Database (Evans 2012) from the 84th (1955-1956)  through 107th (2001-2003) Congresses. 21We choose this time period because it is the only one in which whip count data are publicly available. 22However, we believe that it works well for our analysis for two reasons.First, there are changes in the majority party in Congress, allowing us to analyze the effect of minority leverage on both Republicans and Democratic majorities.Second, this allows us to differentiate between Southern Democrats voting against Republicans, showing true minorityparty disappointments during the period of the Conservative Coalition.
With the prior section in mind, we code our first dependent variable 1 if there is a minority-party disappointment on any amendment pertaining to a given bill, and 0 otherwise.However, we also require that these minority (Republican) disappointments be at odds with Southern Democrats, such that a majority of Southern Democrats opposes a majority of Republicans in each case.We use this variable construction to avoid conflating the effect of cross-party Conservative Coalition proposals with true minority-party proposals. 23We code our second dependent variable 1 if there is a majority-party roll on any amendment pertaining to a given bill, and 0 otherwise. 24Each of these dependent variables captures a form of the concept in our hypothesis: a minority proposal considered on the floor.

21
Bills sometimes change between the whip count and the vote on the bill.In these cases, the whip count data are conservative in identifying a "match" between whip count and bill number, which may cause us to under count the number of bills receiving whip counts.In inferential terms, this means that some bills on which the minority gets the leverage "treatment"in so much as a whip count signals leverageare left in the control condition in our estimation.Thus, the under count, in our case, should make it less likely that we find an effect and our results will thus be conservative estimates.Still, we are working to improve our coding using supplemental sources and expect to mitigate or eliminate this issue prior to publication.

22
We attempt to empirically account for the time period our data cover in two ways.First, we include Congress fixed effects in all of our models.Second, we include Appendix B Table 6 and Table 7, where we subset the data into three different time periods in order to see if our results hold.Our results are consistent across time periods with the exception of the earliest sessions in our data.We believe this result is driven by the limited number of bills during this early period.

23
See Appendix B Table 4 for robustness checks using three variations of the minority-party disappointments variable: (1) binary variable coded as 1 if for a given bill if there was at least 1 amendment where there was a minority disappointment and the majority of southern democrats voted against the minority party; 0 otherwise; (2) proportion of amendments for which there was a minority disappointment and the majority of southern democrats voted against the minority party for a given bill; (3) number of amendments for which there was a minority disappointment and the majority of southern democrats voted against the minority party for a given bill.The results remain in the expected direction for our main independent variable, whip count, and are statically significant at the p < 0.01 level in the models including the binary and count versions of the dependent variables respectively.
We code our main explanatory variable, Whip, as 1 when a majority-party whip count has been taken at least once on a bill, and 0 otherwise. 25Although we are confident is this design, we also include Congress fixed effects and Congress and bill-level controls to alleviate some potential concerns.We also include bill-level controls for (a) the number of days in session when the bill is introduced, 26 (b) the difference in the mean ideological distance between the majority and minority party, (c) the difference in the number of seats between the majority and minority party, (d) whether the president took a position on the bill, 27 (e) whether there was divided government during a given Congress, (f) party unity and (g) the issue area to which the bill corresponds. 28Throughout the remainder of our discussion, the unit of analysis is a House bill with at least one amendment that received a floor vote.We look at the bill level, rather than at individual roll calls, to assess minority-party leverage on a given piece of legislation.Connecting this to our hypothesis more explicitly, we focus on minority-party-favored legislation (specifically amendments) rather than individual votes to examine trends in minority leverage. 29here are 1630 bills that received at least one amendment floor vote during the 84th (1955-1956) through 107th (2001-2003) Congresses. 30For our main outcome variables, 426 bills (26%) had at least one majority roll on an amendment vote and 891 bills (46%) had at least one minority disappointment on an amendment vote.With respect to our main explanatory variable, there were 334 bills (20%) that received at least one whip count. 31bill; (3) number of amendments for which there was a majority-party roll for a given bill.Similar to the results for different variations of the minority disappoints variable, all of the results remain in the expected direction for our main independent variable, whip count, and are statically significant at the p < 0.01 level in the models including the binary and count versions of the dependent variables.
See Appendix B Table 2 and Appendix B Table 3 for three versions of the whip count independent variable: (1) a binary indicator coded as 1 if whip count is conducted, and 0 otherwise; (2) a count indicator of the number of questions where there were whip counts for on a given bill (c) a count indicator of the number of polls taken for all questions associated with a given bill.The results using these different versions of our main independent variable of choice are reported in Appendix.

26
We operationalize plenary time as number of days in session.We assume that plenary scarcity is positively correlated with the number of days in a session that have occurred.This is because each party has policies that it would like to pass but as the session goes on there is less time with which to get those policies on the agenda.27 President position is coded as 1 if the president took a position on a given bill; 0 otherwise.President Position is included as a measure in the PIPC House Roll Call Data (Crespin and Rohde 2018).

28
Bill issue areas are included as a measure in the PIPC House Roll Call Data (Crespin and Rohde 2018).These issue areas include symbolic, appropriations, defense, foreign policy, economy, taxes, and budget, energy and environment, government operations, welfare and human services, and miscellaneous domestic affairs.In Tables 1 and 2, each of these areas is a dichotomous indicator.An example of how these variables are coded is 1 if a bill issue type is symbolic, internal, and procedural, and 0 otherwise for bills dealing with areas of symbolic, internal, and procedural matters.

29
Given that our analysis is at the bill level, the whip indicator shows whether a bill has received a whip count not whether a specific amendment for a given bill has received a whip count.30 Appendix A Table 1 displays the summary statistics for each of the variables used in our analysis.

31
For our control variables the mean days in session when a bill was introduced is 178 days, the mean ideological difference between the majority and minority party (measured on a −1 to 1 scale) is 0.653, the mean difference in size between the majority and minority party during a Congress is 80 seats, the president took a position on 1,475 bills (90%) and there is divided government for 17 of the 24 Congresses in our sample.The issue areas of bills in our sample include 30 symbolic and procedural bills (1.8%), 434 appropriations bills (26.6%), 117 Given our hypothesis, we expect that there will be a positive relationship between minority disappointments and the incidence of a majority whip count.We also expect that there will be a positive relationship between majority rolls and the incidence of a majority whip count.We test this using a generalized linear model. 32

Results
Table 1 displays the results of our generalized linear models predicting minorityparty disappointments including Congress fixed effects. 33In Model 1, we observe that our main independent variable of interest, Whip, is in the expected (positive) direction and statistically significant (p < 0.01).When a majority whip count occurs, there is an 11.85% point increase in the likelihood of a minority-party disappointment on some amendment vote during the consideration of the bill.
In Model 2, we include control variables for the number of days in session when the bill was introduced, difference in mean party DW-NOMINATE scores (Poole and Rosenthal 2007), the margin of seats between the parties, party unity, and whether the president took a position on the bill.Consistent with Model 1, Whip is positive and statistically significant (p < 0.01).There is an 11.91% point increase in the likelihood of a minority-party disappointment on some amendment when a majority whip count is taken on a bill.
Finally, in Model 3, we also incorporate bill issue areas, including Appropriations, Defense, Foreign Policy, Economy, Taxes, and Budget, Energy and Environment, Government Operations, Civil Rights & Justice, Welfare & Human Services, and Miscellaneous Domestic.34Again, Whip is positive and statistically significant (p < 0.01).When a majority whip count occurs, there is a 10.94% point increase in the likelihood of a minority-party disappointment on some amendment vote during the consideration of the bill.
Table 2 displays the results of our generalized linear models predicting majorityparty rolls including Congress fixed effects.These models follow the same structure as those used in Table 1 for minority-party disappointments.In Model 1, our main independent variable, Whip, is in the expected (positive) direction and statistically significant (p < 0.01).When a majority whip count occurs, there is a 19.64% point increase in the likelihood of a majority-party roll on at least one amendment vote while a given bill is being considered on the floor.defense bills (7.2%), 139 foreign policy bills (8.5%), 238 economy, taxes, and budget bills (14.6%), 174 energy and environment bills (10.7%), 186 government operations, civil rights, and justice bills (11.4%), 158 welfare and human services bills (9.7%), and 262 miscellaneous domestic bills (16.1%).

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We include an additional analysis using matching in Appendix B. Matching allows us test our hypothesis for bills that receive and do not receive whip counts while dealing with the potential for insufficient overlap of our covariates.The results of the matching analysis in Appendix B Table 1 and Appendix B Table 2 align with the main findings in the regression analysis.

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Given the dichotomous nature of our dependent variable, we also estimate logit models.The results are consistent with those of the generalized linear model results in Table 1. Figure 2 displays the substantive effects of whip counts on minority disappointments and majority rolls for the predicted probabilities of these models.
Next, in Model 2, we include the same control variables as Model 2 in Table 1.Again, Whip is positive and statistically significant (p < 0.01).Here, when a majority whip count occurs, there is a 19.58% point increase in the likelihood of a majorityparty roll on at least one amendment vote while a given bill is being considered on the floor.
Finally, in Model 3, we include bill issue areas.Once again, Whip is positive and statistically significant (p < .01).When a majority whip count occurs, there is an 18.02% point increase in the likelihood of a majority-party roll on at least one amendment vote while a given bill is being considered.While Tables 1 and 2 display the results of generalized linear models, we recognize that it is also important to examine the predicted probabilities of our main dependent variablesminority disappointment and majority rolls on at least one amendment vote while a bill is being considered.Figure 2 displays the predicted probabilities for minority disappointments and majority rolls when there is a whip count on a given bill.To be clear, we estimate the models including all control variables (Model 3 in Tables 1 and 2) using a generalized linear model with Congress fixed effects and hold all control variables at their means to calculate the predicted probability of a minority disappoint or majority roll when there is a whip count on the bill.When a whip count is taken on a given bill, the probability of a minority disappointment on at least one amendment vote when a bill is being considered increases by 7.8% (44.6 to 52.4%).For majority rolls, there is an increase of 17.1% (22.7-39.8%) in the predicted probability of a majority roll on at least one amendment vote when a bill is being considered.Recall from Fig. 1 that majority rolls on amendments are, in general, very rare; for most of our period, the rate hovers around 10%.Thus, an increase to almost 40% is substantively meaningful.
To sum up, we expected two things: (1) that there would be a positive relationship between minority disappointments and the incidence of a majority whip count, and (2) there would be a positive relationship between majority rolls and the incidence of a majority whip count.That is, in high-leverage situations (where the outcome was believed to be close), if the majority party allowed the minority party to offer one or more amendments, the likelihood of both a majority roll and a minority disappointment should increase. 35This is what we found.In a set of multivariate analyses with or without various controls, our high-leverage explanatory variable (Whip) yields a positive and significant effect.The likelihood of Note: Predicted probabilities for minority disappointments were generated using logistic regression with robust standard errors and congress fixed effects.For minority disappointments, the dependent variable is coded 1 if, for a given bill, there was at least 1 amendment where there was a minority disappointment and the majority of Southern Democrats voted against the minority party, and 0 otherwise.For majority rolls, the dependent variable is coded 1 if, for a given bill, there was at least 1 amendment where there was a majority roll, and 0 otherwise.The explanatory variable is coded as 1 if whip count is conducted, and 0 otherwise.All other covariates were included in the analysis and held constant at their means.
a minority-party disappointment (Table 1) and a majority-party roll (Table 2) on an amendment both increase following a majority-whip count on a bill.

Conclusion
In this paper, we construct a theoretical framework for thinking about minorityparty influence in Congress.In short, we argue that the minority derives leverage by threatening to withhold valuable, pivotal votes to a majority bill at final passage.To secure passage, and in some cases to allow their moderate members to vote against a majority bill that is electorally unpopular in marginal moderate districts, the majority is willing to offer the minority opportunities to have their own proposals considered on the House floor.We argue that, with the goal of recapturing majority status in mind, the minority uses these proposal opportunities to schedule roll calls that help separate them from the majority and force majority-party members into casting difficult votes.
Our datawhich include minority-party disappointment rates and majorityparty roll rates for the Houseshow trends that are consistent with this explanation.Specifically, the minority party seems to use its leverage to get floor votes on many amendment proposals that fail, but with the support of the minority party and the opposition of the majority party.This pattern shows up in the House and stands in contrast to voting on the final passage of bills, which shows very little evidence of any kind of minority proposal.In more systematic multivariate analyses, we find that when a majority whip count occurs on an amendment, the likelihood of both a minority-party disappointment and a majority-party roll increases significantly.
While illuminating, these data and analyses are only a first step in a long overdue enterprise.The role of the minority party in Congress has been largely ignored and has certainly been under theorized in the modern literature on congressional decision-making, especially in the House.Indeed, situating our initial formulation of this theoretical approachand the accompanying analysisin the House provides for a difficult test.As compared to the Senate and many other federal and state legislatures, the minority party's influence in the House is minimal.Thus, exporting this theory to other contexts is likely to be even more relevant for explaining legislative behavior in those chambers.
Consider, for example, an application of this theory in the U.S. Senate.While the "steady-state" influence of the minority party in the Senate is certainly larger than that in the House, our theory suggests conditions when the two will be more similar.Namely, when the prospect for short-term policy gain decrease in the Senatefor example, when the president and the Senate majority are from the same partywe should be more likely to see the minority party use its leverage to get position-taking (rather than policy-making) concessions.
In part, the limited role of the minority in previous theories is almost certainly due to scholars' focus on short-term policy outcomes, without considering the longer policy game.And this is understandable.The "so what" question often dictates the orientation of scholarly literature, and outcome-driven research comfortably passes that test.But the signals sent to voters along the way are intermediate steps in the policy process that certainly help shape outcomes.And, in the end, they help determine who holds the reins of power.For that reason, among others, we believe it is crucial to better understand the contours of minority-party influence in Congress.

Figure 1 .
Figure 1.Minority disappointment rates and majority roll rates on amendment and final-passage votes in the U.S. House, 83rd through the 114th Congresses. 16

Figure 2 .
Figure 2. The effect of whip counts on the probability of minority disappointments and majority rolls.

Table 1 .
Predicting minority-party amendment disappointments GLM estimates with robust standard errors in parentheses and Congress fixed effects.The dependent variable is coded 1 if, for a given bill, there was at least 1 amendment where there was a minority disappointment and the majority of Southern Democrats voted against the minority party, and 0 otherwise.

Table 2 .
Predicting majority-party amendment rolls GLM estimates with robust standard errors in parentheses and Congress fixed effects.The dependent variable is coded 1 if, for a given bill, there was at least 1 amendment where there was a majority roll, and 0 otherwise.