The sentence that uses a subjective pronoun correctly is the first one - Laura and I have written an original play for this year's festival.
The second sentence is incorrect because the word him is not subjective, and neither is her in the third sentence, or them in the last one.
I believe it's the first sentence.
{In disjointed sentences, the cook and the correspondent argued to the difference between a life-saving station and a house of refuge.}
This is the bandwagon technique because they say things like "do what the rest of the country is doing" and other examples of bandwagoning.