How should researchers conduct causal inference when the outcome of interest is latent and measured imperfectly by multiple indicators? We develop a general nonparametric framework for identifying and estimating average treatment effects on latent outcomes in randomized experiments. We show that latent-outcome estimation faces a fundamental but overlooked noncomparability problem due to measurement-set dependence: adding, removing, or replacing measurement targets a different transformation of the latent outcome and therefore a different causal estimand. We formalize the (non)comparability problem and show that common procedures in practice, including standardized averages, principal components analysis, and inverse covariance weighting, generally do not satisfy this condition. To address the problem, we propose a design-based approach built around nonparametric bridge functions. We characterize when such bridge functions exist and derive the corresponding estimator. In simulations with nonlinear measurement systems, our estimator sharply reduces measurement-system dependence relative to standard indices and exhibits good finite-sample performance. We illustrate the method with an application to the Hajj visa lottery. Our framework provides practical guidance for measurement design, identification, and efficient causal estimation with latent outcomes.

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