A Network-Based Measure of Cosponsorship Influence on Bill Passing in the United States House of Representatives

TL;DR

This work introduces a network-based, time-decayed measure of legislator influence derived from bill cosponsorship in the US House. By constructing time-varying, edge-weighted cosponsorship networks with pass and total counts and applying exponential decay, the authors produce party-aware influence scores for each representative and aggregate these to bill-level scores using mean and maximum cosponsor influence. The analysis shows that higher bill-level influence, particularly when using the maximum cosponsor influence, better predicts passage than traditional centrality metrics such as eigenvector centrality, with a notable decline in influence signaling after 2015 as polarization increased. The approach provides a principled proxy for legislator influence from cosponsorship data while acknowledging limitations and suggesting avenues like incorporating topics, committees, and more nuanced centrality comparisons for future work.

Abstract

Each year, the United States Congress considers thousands of legislative proposals to select bills to present to the US President to sign into law. Naturally, the decision processes of members of Congress are subject to peer influence. In this paper, we examine the effect on bill passage of accrued influence between US Congress members in the US House of Representatives. We explore how the influence of a bill's cosponsors affects the bill's outcome (specifically, whether or not it passes in the House). We define a notion of influence by analyzing the structure of a network that we construct using cosponsorship dynamics. We award `influence' between a pair of Congress members when they cosponsor a bill that achieves some amount of legislative success. We find that properties of the bill cosponsorship network can be a useful signal to examine influence in Congress; they help explain why some bills pass and others fail. We compare our measure of influence to off-the-shelf centrality measures and conclude that our influence measure is more indicative of bill passage.

Figures (7)

• Figure 1: A simplistic overview of the legislative process in the United States Congress. A bill starts in the drafting stage of a chamber and then trickles down in that chamber. If a bill passes in its originating chamber, it is introduced in the other chamber and goes through a similar review and voting process. Finally, if the bill passes both chambers, it is sent to the President, who either signs or vetoes the bill. The green and purple arrows indicate the paths of bills that originate in the House of Representatives and Senate, respectively. A bill can fail at any stage of this process.
• Figure 2: Distribution of individual legislators in the US House of Representative in the final month of each Congress.
• Figure 3: Bill-influence time series and the corresponding distributions of relative differences between influence scores of bills that pass and fail in the House of Representatives. In (a), we show bill-level influence that we calculate using the mean of a bill's cosponsors' influence scores. In (b), we show bill-level influence that we calculate using the maximum of a bill's cosponsors' influence scores. In the left panels, we show bill-level influence for 10 years, which we aggregate into nonoverlapping 4-month periods. Each point is the mean influence score of bills in the associated 4-month period starting on the date on the horizontal axis. The values of the bill-level influence scores range between $0$ and $1$. The orange crosses are bills that fail in the House, and the blue disks are bills that pass in the House. The error bar on each marker indicates the standard error. Our computation of influence scores incorporates an exponential decay with a half-life of 6 months. In the right panels, we plot the distributions of the relative differences between the mean influence scores of passed and failed bills. The horizontal axis gives the relative differences between the mean influence scores of bills that pass and fail in the House of Representatives. The vertical axis gives the counts of these relative differences.
• Figure 4: Distribution of the relative differences in influence between passed and failed bills for half-lives of 6, 12, and 24 months. We calculate the influence using the maximum influence score of a bill's cosponsors, and we calculate the relative difference by normalizing the difference between the influence scores of passed and failed bills by the influence scores of the failed bills.
• Figure 5: Eigenvector-centrality time series and the corresponding distributions of relative differences between the eigenvector centralities of bills that pass and fail in the House of Representatives. In (a), we show the bill-level eigenvector centralities that we calculate using the mean of the eigenvector centralities of a bill's cosponsors. In (b), we show the bill-level eigenvector centralities that we calculate using the maximum of the eigenvector centralities of a bill's cosponsors. In the left panels, we show bill-level eigenvector centralities for 10 years, which we aggregate into nonoverlapping 4-month periods. Each point is the mean eigenvector centrality for bills in the associated 4-month period starting on the date on the horizontal axis. The values of the eigenvector centralities range between $0$ and $1$. The orange crosses are bills that fail in the House, and the blue disks are bills that pass in the House. The error bar on each marker indicates the standard error. Our computation of eigenvector centralities incorporates an exponential decay with a half-life of 6 months. In the right panels, we plot the distributions of the relative differences between the eigenvector centralities of passed and failed bills. The horizontal axis gives the relative differences between the mean eigenvector centralities of bills that pass and fail in the House of Representatives. The vertical axis gives the counts of these relative differences.