A Better Way To Measure Representation: The Earth Mover’s Distance

🔍 The measurement problem with mass–elite congruence

Scholars interested in mass–elite congruence—how closely elected elites’ preferences match those of voters—face persistent measurement problems. Current measures can:

• Drop information contained in the full distribution of preferences
• Force arbitrary choices about how to quantize or bin data
• Restrict comparisons to a single dimension, hiding multidimensional mismatches

🔧 What was introduced and why it helps

A new measure borrowed from computer science—the Earth Mover’s Distance (EMD)—is proposed as a solution to these problems. EMD compares entire distributions by calculating how much ‘‘work’’ is required to move one distribution into another, thereby preserving information, avoiding arbitrary quantization choices, and accommodating multidimensional comparisons.

🧭 Where the measure is applied

EMD’s conceptual advantages are demonstrated through applications to two active debates in research on mass–elite congruence:

• Ideological congruence in majoritarian versus proportional electoral systems
• Cross-country determinants of congruence in Latin America

📈 Key findings

• EMD corrects shortcomings of existing congruence measures by using full-distribution information rather than summary statistics or binned data.
• Replacing conventional measures with EMD materially affects inferences in both applied debates above, meaning measurement choices can change substantive conclusions.
• Beyond studies of mass–elite congruence, EMD provides a reliable, general-purpose method for comparing political preference distributions.

💡 Why this matters

Improving measurement with EMD tightens the link between empirical data and claims about representation. Using a distributional, non-arbitrary metric helps ensure that conclusions about ideological congruence or cross-national differences are driven by substantive patterns in the data rather than by measurement artifacts.