🔎 The Problem

Existing ideal-point estimators rely on strong parametric assumptions, leaving no consistent approach to estimation or inference when those assumptions fail. This work offers an alternative that avoids those constraints while preserving meaningful inferences about legislators’ relative positions.

🧭 What the new approach does

• Introduces a nonparametric method for estimating ideal points and conducting inference without imposing strict parametric models.
• Shows that certain comparisons—specifically, inferences about the relative positions of two pairs of legislators—are possible under minimal assumptions.
• Demonstrates how pairwise information can be aggregated across different pair choices to produce estimates and hypothesis tests for all legislators, again without adding further assumptions.

🔧 How the method operates

• Relies on nonparametric identification of relative positions rather than model-dependent scaling or distributional assumptions.
• Uses combinations of pairwise comparisons to expand local inferences into global estimates and formal hypothesis tests.

🧪 Applications to Supreme Court voting

• Applies the nonparametric procedures to two Supreme Court problems:
• Testing for ideological movement by a single justice.
• Testing for multidimensional voting behavior across different decades.
• These applications illustrate the practical usefulness of the methods for real-world roll-call and case-vote data.

📍 Why it matters

• Provides a principled route to estimate and test ideal points when parametric assumptions are untenable.
• Enables robust substantive claims about relative ideology and dimensionality of voting without relying on conventional parametric frameworks.