Abstract
Several prominent theories of legislative organization contend that members coalesce into parties to minimize the collective action problems inherent in pursuing goals that have the character of public goods. Models in that vein ascribe a constrained and primarily reactive role to party leaders, affording them little independent discretion. Such an approach is particularly problematic when considering the nature of public goods pursuits in conjunction with electoral demands for party cohesion and legislative output. Furthermore, the standard treatment of party leadership is inconsistent with empirical findings that party leaders systematically punish disloyalty. The model forwarded herein assumes that party leaders are proactive in shaping members’ contribution decisions by setting punishment levels to produce coalitions of a certain size, but they are always mindful of the overall welfare of the party. I find support for the theoretical propositions derived from my model when examining US House roll-call data over the period of 2001 to 2018.
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Notes
Canen, Kendall and Trebbi (2020) offer an impressive theoretical treatment of party discipline for the purpose of evaluating its effects on party polarization in the US Congress. Their model differs importantly from the one developed below in terms of the motivations for and constraints on party discipline. According to their model, party whips receive rewards for turning out votes for their party, and thus seek to maximize support given the effort costs associated with influencing members’ decisions. Conversely, the model below suggests that party punishment is a tool adopted by leaders to maximize the party’s collective welfare and not simply the size of its supporting coalition. Furthermore, the model developed below departs sharply from Snyder and Ting’s (2002) seminal work on collective party behavior in that party discipline is a strategic choice available to party leaders.
For a vivid account of a US Senate party leader who was particularly demanding of loyalty, see Caro’s (2002) excellent biography of Lyndon Johnson.
Note that the penalty parameter in the following game could instead be conceptualized as the withholding of a reward if one prefers to think of the party leaders’ role as creating incentives rather than deterrents (see, e.g., Pearson 2015).
No constraints bind when punishment is to be administered. As such, the model does not preclude party leaders from batching punishment over a predetermined time horizon. Also note that the common penalty parameter assessed on non-contributors implies that a given punishment is equally costly to all non-contributors, not necessarily that the observed punishments are themselves identical. That is, a particular \(p\) could come in multiple forms across different non-contributors depending on their privately held motivations.
A common value is assumed in the following model since the returns to party-related public goods carry a distinctively universal quality, especially those of the reputational variety (Cox and McCubbins 2007). In fact, Cox and McCubbins (2007, p. 107) find that the average swing to the incumbent’s party is strongly predictive of individual success rates, leading them to conclude that party members experience a “common element” in their electoral fates. However, surely the value of securing a party-related public good is not perfectly uniform across the entire membership. One can adjust the following model to accommodate the existence of heterogeneous values, yielding propositions that are substantively unchanged (see Section A of the Supplemental Appendix).
For any non-uniform distribution with a global maximum (or maxima) less than \(n\), the value of \(g\) satisfying Eq. (4) is decreasing monotonically in \({C}^{*}\). Therefore, any multimodality in the region to the right of the global maximum (or right-most of the global maxima) of \(g\) – the relevant region for the following discussion owing to the selection of the maximum value of the set \(X\) in Eq. (4)—is inconsequential to the results.
The equation can easily be rewritten to account for acquiring the contribution of the nth member, and doing so does not change the following findings.
The marginal increase in the probability that the public good is provided as a result of a member’s contribution (i.e., \(g[C=x])\) is determined by the number of other contributions in equilibrium and therefore is not uniquely assigned to individual members a priori. In that sense, the probability that a given member is decisive is not fixed, as it is often thought to be in many existing models of legislative behavior (e.g., Krehbiel 1998).
To my knowledge, Schickler and Rich (1997) is the only existing study to make a prediction similar to that of Empirical Implication 3. Their argument is rooted in the logic of parties as procedural cartels, whose capacity for punishment depends on the size and internal homogeneity of the caucus. Consequently, party pressure is limited to procedural matters when parties least need to exert influence (Schickler and Rich 1997, p. 1342). I return to that possibility in the robustness checks, where I report evidence consistent with Empirical Implication 3 across all votes, and not just ones relating to procedural matters, and conditions of majority party strength.
Section D of the Supplemental Appendix offers an empirical application to the German Bundestag—a mixed electoral system—in which I examine Member of Parliament (MP) support for party group positions on roll-call votes over the 1958–2013 period. A particular advantage of studying the Bundestag is that it offers a unique opportunity to operationalize the cost parameter by leveraging the fact that some members are elected by way of a closed party list while others are elected from single-member districts. I find results strikingly similar to those reported below. Of particular interest, I find that MPs’ list positions worsen (i.e., numerically increase) when they defect on votes that have widespread support from within their party group.
Stigler’s (1972) contention is at odds with the Minimum Winning Coalition (MWC) thesis positing that rational majorities should minimize the size of their coalition so that the gains from winning can be distributed amongst the smallest possible number of beneficiaries (Riker 1962). However, there is little empirical evidence of MWCs (Fenno 1973; Ferejohn 1974; Manley 1970), and the MWC thesis has received theoretical criticism on various grounds (Butterworth 1971; Shepsle 1974; Weingast 1979). For the purpose of this study, it is important to note that party-related public goods differ by definition from the zero-sum context assumed by the MWC thesis in that they are both non-rivalrous and non-excludable (see Grofman (1984) for a more general critique of the zero-sum assumption).
There were twelve roll-call votes during the period of analysis in which a party was internally tied, and so a majority position could not be determined on these votes. I drop these instances from the analysis. However, including these votes and assigning either yea or nay to the party position does not substantively alter the following results. See Section F of the Supplemental Appendix.
Using other similar and reasonable thresholds to define “low cost” yields substantively similar results.
See Section G of the Supplemental Appendix for more detail on the measurement of these covariates.
The data used for coding issue types were originally collected by Frank R. Baumgartner and Bryan D. Jones with the support of National Science Foundation grant numbers SBR 9320922 and 0111611.
Logging the dependent variable makes it appear more normally distributed and corrects heteroskedasticity problems. The \(\chi 2\) for the Breusch-Pagan test is 629.94 (\(p<0.01\)) for the raw dependent variable and 0.21 (\(p = 0.65\)) for the log-transformed dependent variable.
See Section H of the Supplemental Appendix for the results of models using alternative dependent variables and generalized linear model specifications.
The interaction is necessary to translate the lessons from the one-shot game to the context of accumulated punishment. In order to isolate the effects of MeanSupport, one must also account for the frequency with which a member defects. After all, we would not expect the marginal effect of MeanSupport to be invariant across levels of aggregate party loyalty. That said, the MeanSupport variable remains positive and statistically significant even when removing the interaction term, suggesting that increasing mean levels of support on defections generate more severe punishments (see Section I of the Supplemental Appendix).
Since the number of excluded members is so small (0.3%), it is infeasible to model the selection process (into non-zero defections).
Although the retirement and vote-level variables cannot be included in this model, given the model’s design, the omission of lagged variables is a matter of temporal consideration. However, including the lagged variables in the model does not alter the results reported below. See Section J of the Supplemental Appendix.
Since the statistical significance of interaction terms in nonlinear models may not be properly calculated by standard computational software (Ai and Norton 2003), I confirm the statistical significance of the interaction terms via simulation.
When restricting these models to party unity votes only, the coefficients on Electoral Insecurity and the interaction term grow in magnitude, which we would expect given that party unity votes amplify the tension between individual and collective goals (Carson et al., 2010; Poole and Rosenthal 2007).
Reasonable variation in these percentiles does not substantively alter the results, and selecting more extreme percentiles to characterize member cost types (e.g., 10th and 90th) dramatically increases the disparity in likelihood of supporting party across the cost types.
Using unconditional means (i.e., irrespective of member cost type) for the covariates does not substantively alter the results. However, setting some covariates that account for electoral context (e.g., Spending Gap, Quality Challenger, etc.) to an unconditional mean forces them to assume unrealistic values for the cost types.
See Section M of the Supplemental Appendix for the sensitivity plot. In short, in order to render the effect of Mean Support on Defections statistically insignificant (using α = 0.05), the unobserved confounder(s) would have to explain at least 19.3% of the residual variance of both the treatment and the outcome, which seems exceedingly unlikely. Furthermore, using Lagged Vote Share as a benchmark for assessing the strength of the confounder(s) needed to undo the statistically significant effect observed for the Mean Support on Defections variable, since Lagged Vote Share has one of the largest standardized effects of any covariate in the model and has clear theoretical implications for party discipline, I find that the confounder(s) would need to be more than 58 times the size of Lagged Vote Share. Therefore, this analysis suggests that an unobserved confounder(s), which almost certainly exists in any observational study, is unlikely to disrupt the core findings.
The average incumbent spent roughly $1.34 million on campaigns during the period of analysis (with a standard deviation of $1.24 million). Therefore, it stands to reason that punishments (or the threat thereof) of this magnitude are consequential to members. Perhaps more important, I also find a positive relationship between lagged punishment and members’ probability of supporting their party, providing at least some circumstantial evidence that punishments of this variety resonate with members in terms of their future behavior (see Section N of the Supplemental Appendix).
Note that a small fraction of members in this analysis (approximately 19%) have party agreement scores below 0.91—the maximum marginal effect—and so most members fall in the region of party agreement scores where increasing levels of party agreement mitigate the punishment associated with a given value of mean party support on defections.
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Acknowledgements
Special thanks to Martin Battle, Nicole Huffman, Steven Smith, and the participants of the “Analyzing Parties in Congress: Whips, Pivots, & Party Leaders” panel at the 2021 Meeting of the Midwest Political Science Association.
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Vander Wielen, R.J. Party leaders as welfare-maximizing coalition builders in the pursuit of party-related public goods. Public Choice 194, 75–99 (2023). https://doi.org/10.1007/s11127-022-01017-w
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DOI: https://doi.org/10.1007/s11127-022-01017-w