Exploring ideological signals from cosponsorship

ABSTRACT

While cosponsorship is a useful tool for cosponsors, what is its impact on the bill? Adapting the mathematical concept of directed transportation networks for the American Congressional context, we suggest cosponsorship’s impact on a bill comes in the form of an ideological signal. We offer a model of policymaking where ideological “weight” is added to bills each time legislators sign on as cosponsors. In addition to policy substance, the bill’s final position in ideological space may also be considered as a function of all collaborators (i.e., initial sponsor and cosponsors). We conclude by extending and applying our model to two bills from the 115th U.S. House. Results comport with our model’s expectations, suggesting we are capturing ideological signals from cosponsorship.

KEYWORDS:

• Minimal directed transportation networks
• bill cosponsorship
• American politics

Acknowledgments

We would like to thank Leonardo Antenangeli, Eric Arias, Jeff Harden, Justin Kirkland, Markie McBrayer, Jon Slapin, Craig Volden, and participants at the 2018 Joint Mathematics Meeting for many helpful comments and feedback on several iterations of this project. All remaining errors are our own.

Notes

¹ While legislators are sometimes assigned to bills as sponsors after committee mark up, for example, distinguishing between types of sponsors, whether “bill managers” (i.e., (sub)committee chairs (Hall & Evans, 1990)) or original sponsors, is beyond the scope of our task. We begin at the point where a bill has a sponsor, regardless of how the sponsor came to be on the bill.

² Importantly, we recognize the assumptions in our supposition to this point. However, our goal here is not to offer a fully developed theory, but rather a new approach to demonstrating the shipping of ideological weight through Congressional cosponsorship. Thus, with this brief extension, we are interested in providing sufficient, though admittedly limited context with enough face validity to justify a plausible extension of our baseline model.

³ We reiterate that we have restricted $v$ to some compact interval on the $x$-axis, so that the following constructions simultaneously demonstrate both the basic model and all possible target intervals for the extension.

⁴ For each collaborator $w_i$, $p_i=1$; however, in the following subsection we will need a more general perspective allowing for weights to be other natural numbers. So, we introduce this notation now for convenience.

⁵ One must use caution when applying this technique if the topology has degeneracies. See footnote B.6 for more explanation.

⁶ We only gave an example construction for a full topology (i.e., a topology with one less branching point than the number of collaborators). Sometimes a topology with degeneracies may be minimal. Degeneracies may occur due to the different minimal shapes in Theorem 2.6. In these cases, the “top pivot” point will need to be defined appropriately since Theorem 2.5 only holds for networks with three edges. However, there is always a well-defined “top pivot” point corresponding to each topology (with or without degeneracies). One should use caution in the constructions. Regardless, one may always use a numerical approximation technique similar to that described in Xia (2007).

⁷ This is why the policy score and the cosponsorship score are identical in the base model.

⁸ While typically there will be only one minimal path using the above definitions, it is possible to have non-uniqueness. Within our context, however, it is doubtful that this will occur since it requires a significantly high level of symmetry.