Design an experiment to test the causality in a bidirectional relationship between two variables.

Instruction: Outline an experimental or quasi-experimental design that can differentiate causal directions between two interacting variables.

Context: The question assesses the ability to design studies that can unveil complex interactions and causal directions between variables.

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Define both variables as manipulable quantities or policies with a time order. For a recommendation system, personalization is the assigned algorithm policy; click-through rate is an outcome influenced by that policy and user behavior, not the policy itself.

First randomize users to specified personalization policies, freeze or log training updates, and measure later engagement over a fixed window...

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