  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.
