Three people are discussing something. One of them asks another to be judge on who's right.
What's the exact meaning of 来 here? Since three of them are already together, it shouldn't be "come here".
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You are right, we shouldn't take its literal meaning here "to come here".
来, here in the context, is used to invite for comment. Other examples: 让我来(let me do it or I will cover it). 你来(You do it). 不，我不来(No, I won't do it.)
This dictionary definition addresses it:
用在动词性短语前面，表示要做某事(preceding a verbal phrase, denoting will do something)
E. g. 我来说几句。
Person A or B calls person C to 'come' judging the issue because the issue is right in front of them
Notice, we use [来 + V] when the object is close to us, and we use [去 + V] when the object is not close to us
我來開車 (the car is close by or you are in the car)
我去開車 (the car is not near by or even insigh)