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But it doesn't sound like a False Dichotomy to me, unless Papa Cunningham is lead to believe that Joanie must wear one of the two dresses and there are no alternatives.
I'd actually consider it an In-Universe version of Censor Decoy, really.
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The scene in "Happy Days" where Joanie models the extremely risqué prom dress for Papa Cunningham so he'll approve the slightly risqué dress Joanie actually wants to wear - is that an example of False Dichotomy, or more of a Gambit? I couldn't find a matching gambit :/