We study the design of multi-arm experiments that identify local average treatment effects under imperfect compliance. With three or more arms, conventional randomization fails to identify margin-specific effects even under strong extensions of monotone compliance. A choice-theoretic analysis unifies these extensions and motivates a two-stage design: subjects report a preferred arm and are randomized conditional on it. If treatment is confined to the assigned or reported arm, one-sided noncompliance is restored conditional on the report, identifying the effect between the two for their compliers. We discuss the design's applicability and feasibility in relation to the choice model.

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