The public was shocked at the apparent unfairness of the ______ sentence;…

In a two-blank sentence-completion item, a signal word such as “however” marks a contrast between the two clauses: the first clause states one viewpoint, and the word after the contrast signal must express a related but distinct idea from a different vantage point, even when the two chosen words are close synonyms in a dictionary sense.

Here the first clause is about how the sentence LOOKED to the public — unfair and unpredictable — so the first blank needs a word meaning “based on random will rather than reason,” which is ‘arbitrary’. The clause after ‘however’ reframes the same ruling from the legal scholars’ point of view: it is simply an exercise of the judge’s own lawful judgment, which is exactly what ‘discretionary’ (relating to discretion, the power to decide within one’s own judgment) names. So the sentence contrasts how the ruling APPEARED (arbitrary) with what it actually WAS in legal terms (discretionary) — the two words describe the same act from two different perspectives, which is the hallmark of this kind of sentence.

Checking the other pairs against both blanks together confirms none fits as cleanly: a word meaning ‘wise’ does not capture the legal notion of a judge’s own decision-making power; a word meaning ‘fair’ would remove the very contrast the sentence sets up; and a word meaning ‘biased’ contradicts a judge’s legitimate role rather than explaining it.