ה' אלו"הינו

I've just heard something which I found interesting which I know is one of those things that would fall away after a while like the other residue in my mind had it not been for the fact that I am so close to a computer. Praised be G_d.

I heard that monarchs and other rulers in the past were called and called themselves by the third person plural (for example saying "we" instead of "I") because they felt that in a sense, they encompassed in themselves the entire nation they were ruling over.

I was just thinking of how that might apply to some of the attribute names with which we refer to G_d at times in Hebrew. אלו"הים for example, is said to also mean judge (as אלו"ה wouldn't). In this case it would mean a judge who encompasses his judged. Is that somehow eluded to when referring to G_d as a judge in this ancient Hebrew third person plural?