Agreeing to the blindfold is also agreeing that they will not be able to reliably identify their partner. The sex worker knew that up front.
Here’s some scenarios for you:
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A cop pays for sex with a prostitute. The subject of his job never comes up. He pays and leaves. The prostitute is not arrested, nor does she ever know he is a cop.
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A cop pays for sex with a prostitute. The subject of his job doesn’t come up. Before leaving the cop says, “By the way, I’m actually a cop.” There is no mention of arrest.
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A cop pays for sex with a prostitute. The subject of his job doesn’t come up. Before leaving the cop says, “I’m a cop, and you’re under arrest”. She is arrested for prostitution.
Now under which of those has rape been committed?