The Dimensionality of Congressional Voting Reconsidered

• Published date: 01 September 2016
• DOI: 10.1177/1532673X15608940
• Date: 01 September 2016
• Author: Steven S. Smith,Stephen R. Haptonstahl,Jason M. Roberts
• Subject Matter: Articles

American Politics Research

2016, Vol. 44(5) 794 –815

© The Author(s) 2015

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DOI: 10.1177/1532673X15608940

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Article

The Dimensionality of

Congressional Voting

Reconsidered

Jason M. Roberts1, Steven S. Smith2,

and Stephen R. Haptonstahl3

Abstract

This article reports findings for a decomposition of the roll-call voting record

of the U.S. Congress to determine the effect of the level of aggregation on

the observed dimensionality of the policy space. In doing so, we identify

some but certainly not all of the ways in which the aggregation of the voting

record affects the observed dimensionality of the policy space. For the 1955

to 2008 period (84th-110th Congresses), we apply optimal classification

(OC) to votes aggregated to the level of the individual bill and policy area to

measure dimensionality. We examine the marginal proportional reduction in

error (MPRE) across dimensions. Our results demonstrate that complexity

in voting patterns of individual bill episodes is the norm, that aggregating

to higher levels reduces the observed dimensionality, and that the liberal–

conservative dimension appears more dominant in more highly aggregated

analyses. These results call into question many of the conclusions from

the theoretical and empirical literature on the U.S. Congress that uses a

unidimensional model.

Keywords

Congress, roll call voting, dimensions

1University of North Carolina at Chapel Hill, USA

2Washington University in St. Louis, MO, USA

3National Public Radio, Reston, VA, USA

Corresponding Author:

Jason M. Roberts, University of North Carolina at Chapel Hill, 361 Hamilton Hall, CB 3265,

Chapel Hill, NC 27599, USA.

Email: jroberts@unc.edu

608940APRXXX10.1177/1532673X15608940American Politics ResearchRoberts et al.

research-article2015

Roberts et al. 795

Introduction

The dimensionality of congressional voting behavior is critical to the devel-

opment and application of spatial voting theories to congressional policy

making. Yet, the dimensionality of voting in the U.S. Congress remains a

contested empirical issue. Numerous studies in the literature on the U.S.

Congress assume, either implicitly or explicitly, that one or at the most two

dimensions can characterize the underlying policy space. However, as we

demonstrate in this article, the clear patterns of unidimensionality that are

often observed in voting aggregated to whole Congresses are not duplicated

when the unit of analysis is the individual bill or subsets of bills. In fact, we

find considerable evidence that multidimensionality is the norm for most

major bills and policy areas across both the House and Senate. This is an

important point, as most theories and applications of spatial voting models to

Congress deal with particular bill episodes or policy areas, not aggregations

of votes over an entire Congress. Our findings suggest that much of this

research incorrectly assumes low dimensionality, rendering many of the

empirical findings potentially suspect.

In this article, we report findings for a decomposition of the roll-call vot-

ing record. In doing so, we identify some but certainly not all of the ways in

which the aggregation of the voting record affects the observed dimensional-

ity of the policy space. For the 1955 to 2008 period (84th-110th Congresses),

we apply optimal classification (OC) algorithms to votes aggregated to the

level of the individual bill policy area to measure dimensionality. We exam-

ine the marginal proportional reduction in error (MPRE) across dimensions.

Our results demonstrate that complexity in voting patterns of individual bill

episodes is the norm, that aggregating to higher levels reduces the observed

dimensionality, and that the liberal–conservative dimension appears more

dominant in more highly aggregated analyses.

Dimensionality and Theories of Legislating

In studies of legislative behavior, it is well understood that there are funda-

mental differences between unidimensional and multidimensional spaces.

Unidimensional policy spaces are well-behaved—pivotal legislators such as

the median can be readily identified. Multidimensional policy spaces, how-

ever, generally do not have identifiable pivots. Consequently, outcomes are

predicted with great precision in unidimensional space, whereas in most cases

multidimensional spaces do not offer precise predictions and can lead to the

possibility of cycling or chaos. For this reason, most empirical applications of

spatial theory assume unidimensionality (Cameron, 2000; Krehbiel, 1998).