Existing approaches to estimating politicians' latent positions along specific dimensions often fail when relevant data is limited. We leverage the embedded knowledge in generative large language models (LLMs) to address this challenge and measure lawmakers' positions along specific political or policy dimensions. We prompt an instruction/dialogue-tuned LLM to pairwise compare lawmakers and then scale the resulting graph using the Bradley-Terry model. We estimate novel measures of U.S. senators' positions on liberal-conservative ideology, gun control, and abortion. Our liberal-conservative scale, used to validate LLM-driven scaling, strongly correlates with existing measures and offsets interpretive gaps, suggesting LLMs synthesize relevant data from internet and digitized media rather than memorizing existing measures. Our gun control and abortion measures -- the first of their kind -- differ from the liberal-conservative scale in face-valid ways and predict interest group ratings and legislator votes better than ideology alone. Our findings suggest LLMs hold promise for solving complex social science measurement problems.

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