🧭 Framing the Debate: Scholars debate two related questions about political preferences: how constrained preferences are, and whether they lie on a single left–right spectrum or require multiple dimensions. Insufficient formalization has often led researchers to treat a lack of constraint as the same thing as multidimensionality. This paper refines the concepts of constraint and dimensionality in a formal framework and shows how they imply different, testable patterns in observed preferences.

🔧 How measurement was rethought: A cross-validation estimator is introduced to separately measure constraint and dimensionality inside canonical ideal point models. The estimator is motivated by the theoretical distinctions and converts those distinctions into distinct empirical implications that can be evaluated in real data.

📊 What was analyzed:

• Data come from both the mass public and elected politicians in the United States.
• Analysis uses canonical ideal point modeling augmented with the new cross-validation estimator to assess whether preferences are constrained and whether they are multidimensional.

✨ Key findings:

• American political preferences are best described as one-dimensional.
• Politicians display substantially more constraint in their preferences than the mass public.
• The gap in constraint between politicians and the public cannot be attributed to differences in agendas or to the incentives faced by the different actor types.

❗️ Why it matters: By separating the concepts of constraint and dimensionality and providing a practical estimator, the paper clarifies a long-standing ambiguity in studies of public opinion and legislative behavior. The results imply that one-dimensional models remain appropriate for American politics, while highlighting systematic differences in how constrained elites versus the public are—an important consideration for theories of representation and political choice.