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One man or person can represent “a multitude of men.”
A multitude of men are made one person when they are by one man, or one person, represented; so that it be done with the consent of every one of that multitude in particular. For it is the unity of the representer, not the unity of the represented, that maketh the person one. And it is the representer that beareth the person, and but one person: and unity cannot otherwise be understood in multitude.
Hobbes, Lev XVI 13
The representative’s actions are “owned” by everyone represented.
And because the multitude naturally is not one, but many, they cannot be understood for one, but in any authors, of everything their representative saith or doth in their name; every man giving their common representer authority from himself in particular, and owning all the actions the representer doth, in case they give him authority without stint: otherwise, when they limit him in what and how far he shall represent them, none of them owneth more than they gave him commission to act.
Hobbes, Lev XVI 14
A monarch or assembly member represents both himself and the State.
A public minister is he that by the sovereign, whether a monarch or an assembly, is employed in any affairs, with authority to represent in that employment the person of the Commonwealth. And whereas every man or assembly that hath sovereignty representeth two persons, or, as the more common phrase is, has two capacities, one natural and another politic; as a monarch hath the person not only of the Commonwealth, but also of a man, and a sovereign assembly hath the person not only of the Commonwealth, but also of the assembly: they that be servants to them in their natural capacity are not public ministers; but those only that serve them in the administration of the public business. And therefore neither ushers, nor sergeants, nor other officers that wait on the assembly for no other purpose but for the commodity of the men assembled, in an aristocracy or democracy; nor stewards, chamberlains, cofferers, or any other officers of the household of a monarch, are public ministers in a monarchy.
Hobbes, Lev XXIII 2