Measuring party loyalty

Measuring party loyalty (DOI: https://doi.org/10.1017/psrm.2025.10083) was written by Adam J. Ramey in 2026. It was published in Political Science Research and Methods.

The author notes the 2015 Republican revolt against Boehner cannot be explained by current theory.

• "Ideal point estimation methods of both the Poole and Rosenthal (1997) and Bayesian flavors ([Clinton, Jackman and Rivers, 2004]) have shown increased within-party voting homogeneity over the last two decades."
• Party loyalty measures like Party Unity Scores (Brady, Cooper and Hurley, 1979) are similarly high
  • "23 of the 25 legislators who voted against Boehner had Party Unity Scores that were just as high, if not higher, than the members who voted for him"

The author argues that these measures are flawed because they each make a simplifying assumption about legislator behavior. In some cases it is assuming that legislators do not have preferences, so every vote is an indication of loyalty. In other cases, that party leadership only cares about close votes.

Let:

• i index the N legislators

• j index the J roll call votes

• t index the T time periods

Each legislator i has a 1-dimensional preferred policy point as x_i, and has a utility function in terms of a policy point θ (given their own preferred point) as u_i(θ | x_i) = -(x_i - θ)² + ε. Assume ε is normally distributed.

For each roll call vote j, there is a binary decision from each legislator i as y_ij (1='yea').

• To further simplify notation: when evaluating the utility of a legislator (u_i(θ | x_i)), let θ = ψ_j if a given legislator votes 'yea', vs θ = ξ_j if they vote 'nay'.

• Absent party pressure, this binary decision is made off of the utility function.

  • i.e., vote 'yea' if -(x_i - ψ_j)² + ε_ij ≥ -(x_i - ξ_j)² + ε_ij'

• If the party is revealed to care (indicated by ρ_j=1) then each legislator has an additional shock term as b_ij(x_i). While this term may be uniform across legislators, it may also vary with respect to e.g., group identifications as moderates or extremists.

  • i.e., vote 'yea' if -(x_i - ψ_j)² + ρ_jb_ij(x_i) + ε_ij ≥ -(x_i - ξ_j)² + ε_ij'

This model can be formulated in the style of IRT, where β_j = 2(ψ_j - ξ_j) is item discrimination and α_j = ψ_j² - ξ_j² is item difficulty.

Model identification now depends on knowing ρ_j and b_ij.

Author re-uses the dataset from Asmussen and Ramey (2018). Some roll call votes involve both party leaders taking positions, others involve only a Republican position, and others involve only a Democrat position. This variation allows measurement of legislator-specific party loyalty.

For each roll call vote j, let s_ij indicate the party position for the party of legislator i. This takes on value 1 if the party position is 'yea', -1 if 'nay', and finally 0 if no position is taken. Furthermore let δ_i,t[j] be party inducement; it is assumed to be symmetric whether the party's position is 'yea' or 'nay', but it is allowed to vary over legislators and over time (t looked up based on j). The model is now Φ(β_jx_i - α_j + δ_i,t[j] s_ij).

"Table 3 identifies some of the roll calls for which this model produces substantially increased numbers of correct predictions. As we see in the table, some of the most contentious votes from the last two-and-a-half decades are present in the list, including the General Agreement on Tariffs and Trade (GATT), the Homeland Security Act, the Omnibus Budget Reconciliation Act of 1990, and the reauthorization of the Export-Import Bank. Additionally, two votes that sought to invoke Section 5(c) of the War Powers Resolution to remove U.S. troops from Libya and Afghanistan are present."

More generally the author finds that:

• Democrats feature higher party loyalty on average
• the majority party at any time features higher party loyalty

Reading notes

Going to need some time to digest this, probably will try to replicate first.

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