In the given question a sentence is given with a blank and you have to choose an appropriate word from the given options that can fill the sentence making that grammatically and meaningfully complete. Dissent is an inevitable casualty when democracy is constructed as majority rule;_________________ perpetuate the myth of majoritarianism.

The sentence talks about dissent being a casualty when democracy is framed as majority rule. The phrase "in order to" is used to indicate purpose or intention. It suggests that the action of perpetuating the myth of majoritarianism happens for a reason or purpose, i.e., "in order to" perpetuate the myth of majoritarianism. Resembling does not fit as it implies similarity, which doesn't make sense in this context. Like to is grammatically incorrect in this context.                        Either to doesn’t align with the intended meaning of purpose in the sentence.