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The “but you are free” (BYAF) compliance-gaining technique operates by telling the target that he or she is free to refuse the request. A meta-analysis of 42 studies of the effectiveness of that technique indicated that it was an effective means of increasing compliance rates in most contexts. It was effective regardless of type of request, but effectiveness diminished when the decision to enact the target behavior was not made immediately, consistent with a self-presentation explanation of the technique's effectiveness.
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Christopher J. Carpenter (2012) studied this question.
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