Ordinarily, who gets the first shot at forming the government should not…

This question is a double-blank vocabulary-in-context item: the correct pair of words must fit both the grammar of the sentence — the first blank needs a verb that collocates with the preposition 'in' (as in 'engage in doing something'), and the second blank needs a noun that can serve as the direct object of the gerund 'engineering' (i.e. something that is 'engineered') — and the meaning implied by the rest of the sentence; a word that is grammatically valid but semantically wrong for the context is not the answer.

The sentence draws a contrast: normally it should not matter which group gets the first chance to form the government, unless that group is doing something improper — 'if neither group [blank 1] in engineering [blank 2]' — in which case the fair way to decide is a confidence vote on the floor of the House. The improper conduct being contrasted with a floor vote is well known in parliamentary politics: one side actively bringing about a shift in legislators' allegiance (through inducement or pressure) to muster a majority outside the House. 'Engages' (actively undertakes/participates in) together with 'defections' (legislators abandoning their own party to join a rival camp) names exactly this manoeuvre — a party 'engineering defections' rather than letting numbers be tested fairly on the floor.

• indulged; infections — 'infections' belongs to illness/disease, not to political manoeuvring for government formation; the phrase has no connection to the sentence's subject.

• involves; defaults — 'defaults' means failing to honour a financial or contractual obligation (e.g. a loan default); it has nothing to do with legislators switching political sides.

• participates; mistakes — 'mistakes' implies an unintentional error, but the sentence is contrasting a deliberate strategy to swing numbers with a fair floor vote; an accidental blunder does not fit that contrast.

Only 'engages; defections' satisfies both the grammar and the political sense of the sentence, so it is the correct pair.