As an expression of Hobbes’ philosophy and political theory, The Leviathan represents a framework for the establishment and maintenance of a political system based on a number of underlying assumptions about the way in which humans interact with each other. Hobbes progresses from a cynical and decidedly negative assessment of human nature and a resulting a priori conclusion about a hypothetical unincorporated, pre-political state of human affairs to an assessment of the most effective scheme for political organization.
He argues that the fundamental duty of a government is the preservation of order and to provide an alternative to the chaotic and violent state of nature. In addition to the motivations for forming a government that subordinates individual freedom to that of society as expressed (at least as Hobbes would prefer) through a sovereign tasked with keeping order, Hobbes also details the notional mechanisms through which that power consolidates and the necessary interactions among members of a group to organize collectively as distinct from their state as individuals.
The way in which individuals come together to express their preference for order over violence through a contractual relationship with one another forms an important part of Hobbes’ theory, especially as it relates to other views on democracy and political organization. As a claim, the necessary political organization is born through collective agreement among citizens to cede individual rights to the group; uniquely, Hobbes says that we cede rights in turn to one another and in that act of incorporation become tantamount to a single (artificial) person for whom things are expressed with a spokesperson.
One of Hobbes fundamental claims is that incorporation of members is a necessary step in political organization as individuals leave a natural state into an organized one and incorporation requires personation. Indeed, Hobbes insists on the inseparable nature of those being represented and that which represents them. He goes to far as to say that we cannot speak of the united group without the manifestation of a representative because “it is the Representer that beareth the Person, and but one Person: And Unity, cannot otherwise be understood in Multitude. 
In our departure from the theoretical state of nature which is a supposedly fictional (but perhaps realized, as Hobbes suggests, in states whose political systems destabilize and leave humans without the necessary checks on behavior) we as citizens come together. In order to form a group, we make ‘covenants’ among ourselves and decide to cede rights to each other. The covenant that Hobbes regards as the mechanism for political organization into a commonwealth is a covenant among (soon to be) citizens, the individuals that make up the “great Multitude” and thus enter into “mutuall Covenants one with another”.
Following this, the group becomes a single body and has the same properties as a person, but of course is something artificially created. By this, the group comes to an artificial person. For that person to function, however, it needs some manifestation of itself in order to embody the actor. Specifically, if the group wishes to perform the actions required to classify itself as an incorporated person, it requires some representation. This ought manifest as a single person: if the group is represented by a single individual actor, according to Hobbes, that person personates the group as a sort of representative.
The group then takes on a unified responsibility that is likewise manifested in that individual. In application, the group is personified under a legal system wherein the law treats the entire group as a single person. Functionally, though the claim is primarily notional and thus impossible to verify empirically, the underlying case that some form of personation is required as an function of incorporation would seem to suggest that it functions as a logical outgrowth of that incorporation.
Interestingly, this leads to different perspectives as to who is personating on behalf of whom or as whom. So, for Hobbes, the ideal manifestation of the group is in a sovereign, but this leads to questions of to whom this representer functions. Naturally, from the perspective of those in the group, the representative is the embodiment of themselves as they have incorporated with others. Also though, this means that the representative is a sort of representation of them as individuals because it is (at least under the Hobbesian definition) a part of the individual’s will to incorporate.
Thirdly though, one could say that to an outside observer, perhaps an individual in another state observing this newly formed hypothetical state as it emerges from the chaotic state of nature into an organized political system, that the Monarch qua representative is a personation of both the body of individuals as a new, distinct person, but is also a representation of the individuals who make up that body. This has implications for the power structure that unfolds a function of the relationship between the governed and governor.
The relationship between the corporate body and the individual who represents them suggests a decidedly asymmetric relationship. The much maligned alternative being the state of nature, it is argued by Hobbes that any state power, no matter how oppressive, is entirely superior to alternative and as rational actors who are inherently self-interested (as Hobbes supposes we all are) it is logical and right to prefer even the most despotic system. The asymmetry becomes an outgrowth of responsibly and representation.
In the Hobbesian framework, representation is not about the Monarch qua representative being accountable to those whom she represents, but rather it allows that individual to act freely while still maintaining the role of the manifestation of the corporate body. In this way, she (the representative) functions like an independent actor, but is still inextricably linked to the larger body whom she represents. The sovereign is not, therefore, an agent of the people because there would require some adjudicating mechanism to establish when or how the agreement between (or among) the sovereign and those whom she rules is breeched.
The sovereign qua representative is granted full autonomy even as an actor who represents the body and that cannot be undermined: “he that doth any thing by authority from another, doth therein no injury to him by whose authority he acteth”.  The represented (the subjects) are thus subjected to the actor but are still, paridoxically, responsible for the actor insofar as she is a manifestation of the group. Hobbes writes, “For that which the Representative doth, as Actor, every one of the Subjects doth, as Author”.  The contractual agreement is arranged such that individuals enter into the agreement with one another, though.
This means that individuals have duties to one another but the sovereign has no duty, says Hobbes, to them because the sovereign has made no explicit deal with the individuals in the group and her role emerged as logical outgrowth of the incorporation. This goes even further though, because the covenant in which individuals enter requires that they may be forced to give up ownership of their own property and in the case of coercion by the sovereign, their individual will. At the same time, they are individually responsible for the representative’s actions because she is the group.
Even still, Hobbes holds that this strange relationship is is far preferable one to the state of nature wherein no individual can make a just claim to any property or right, even to life. As has been established, the primary contractual relationship is not between an individual and a sovereign, but rather from an individual to the other individuals with whom she is incorporated. In Hobbes’ conception, the sovereign thus acts not as an outside entity upon the incorporated group, but rather as an embodiment of it. The commonwealth that Hobbes describes is not, at least in its inception, an agreement between subjects and the monarch.
Indeed, that would be impossible, as the underlying claim on which this discussion is based suggests, that individuals could make a compact with their ruler when the ruler is a result of the compacts individuals make with one another. This has implications for those who would complain about the sovereign. They are not bound to follow the sovereign because of an agreement they made with her, but rather because of the agreement they made with the other subjects (albeit a tacit agreement or a function of forceful conquest). The representative sovereign is only the embodiment of the government, even though she may behave like an individual actor.
Thus far, the only discussion has been around a monarchical political organization as that is the mode which Hobbes demonstrably prefers. As it pertains to other conceptions of political organization, the Hobbesian framework necessarily discounts any form of government not fully embodied in one of the three systems he and other political theorists outline. Specifically, mixed forms of government that seek to combine democracy, monarchy, and oligarchy are inherently flawed. Namely, a mixed constitution is fundamentally impossible and is only a state of conflict that has temporally stalled but is ultimately unstable.
This is because the monarchy as a representative provides a system for clear personage: The resolutions of a monarch are subject to the inconstancy of human nature; but in assemblies contrary opinion undoes today all that was concluded yesterday. … A monarch cannot disagree with himself; but an assembly may; even sufficient to produce a civil war.  Thus the flaws inherent to other systems are problems with human nature as we seek to interact with each other and develop conflict. Non-pure forms of other systems are only worsen the flaws that come with them.
He argues that the powers that government is designed to function with (legislation, judiciary adjudication, taxation, peacekeeping/war, etc. ) are linked to each other such that they cannot function efficaciously without the other. Moreover, leaving different areas in the hands of different political systems only fragments and worsens the ability of the organizational structure to function. Hobbes calls the requisite powers the “essential rights of sovereignty” with which decision making must rest in a single individual to avoid some sort of deadlock or conflict.
To avoid the horrible prospect of institutional collapse thus a devolution into the state of nature, citizens are duty bound to themselves and to each other treat sovereign as having absolute authority. As a question of legitimate governmental authority, Hobbes’ unique conception of free will (one which remains free even under conditions we would call ‘duress’) means that legitimacy is not a function of how the government came into existence, but rather how it maintains itself.
Liberty, he says, is in the freedom of motion and unless one is literally “encumbered” with chains, she is free to act. Even under the immediate threat of violence, a decision to yield is an act of agreement. As it pertains to the state, the same coercion applied by the sovereign still is not a constraint on liberty. This authority remains legitimate. Theoretically, one still has ought to have the right to protect one’s self as that is why she has chosen to leave the state of nature, but this protection can only come through a sovereign, so the question becomes cyclical.
Even different ways in which the sovereign takes rule is inconsequential to one’s obligations towards her as the representative. The social covenant involves both the renunciation or transfer of right and the authorization of the sovereign power. The legitimacy is predicated upon the absence of the state of nature and thus on the sovereign’s ability to impose order. At its logical extreme, the presence of any sovereign would be an outgrowth of the decision for the body to incorporate and therefore signals the departure from the natural state.