Which pronoun correctly refers to both judges in the sentence: "Both of the judges have made (his or her, their) opinions known"?

The use of "their" is appropriate in this context because it serves as a plural pronoun that can refer back to the plural antecedent "both of the judges." In modern English, "their" is increasingly accepted as a singular, gender-neutral pronoun that encompasses individuals regardless of gender, making it a versatile choice in the sentence provided.

This choice also aligns with the idea of inclusivity, allowing for references to individuals without the necessity to specify gender. In contrast, "his or her" can be awkward and lacks the fluidity that "their" provides, especially when addressing a mixed-gender group. "Its" would be unsuitable as it refers to non-human entities and cannot correctly apply to people. Lastly, "his" is also incorrect because it assumes that both judges are male, which does not embrace the potential for diversity in gender. Thus, "their" effectively and accurately communicates that the opinions of both judges have been expressed, aligning perfectly with the plural subject.