The narrator of "Shooting an Elephant" (a semi-autobiographical Orwell, speaking via his own experiences) fulfills the role of "ruler". The Burmese citizens are the "ruled". However, we might benefit by breaking down these terms even further.

There is both an abstract idea, and an embodiment, of the terms "ruler" and "ruled". In a sense, the abstract body of the British government is the actual ruler; the narrator is merely a person who happens to be acting on its behalf. He is no more a ruler than any other person, it is only by virtue of his birth as an English citizen that he happens to be on the ruling side. This, his reluctance for his position, and his love/hate relationship with the Burmese, complicate his identity as a ruler, and contribute to the modernist tone of the story.

Likewise, the role of "ruled" is complicated by the fact that the narrator is, largely, set against the entire town, and the people are the driving force behind the action. They caused the narrator to be worried for his pride, and his perception of them as distasteful "little beasts" make them seem less like rational humans, and more like temperamental animals; ruling them is more like herding them.

Thus, the roles of ruler and ruled are complex, and paradoxical; while the narrator is ostensibly the ruler and the Burmese the ruled, by virtue of their political relationship, the narrator in fact does not want to rule the Burmese (he even advocates on their behalf against the British), yet fulfills his duty more out of habit and a sense of pride instilled in him by his own society, not the Burmese. We might even see the narrator as the "ruled" himself, his rulers being both the Burmese population and the expectations of British society itself.

What are the roles of the ruler and the ruled in "Shooting an Elephant"?

George Orwell's essay is both an indictment against the tyranny of imperialism and the invidious resentment of those who are subjugated. Orwell writes of the hatred toward the conquered that emerges in the rulers accompanied by an emerging hatred among the conquered for the stronger oppressor. The difference between ruler and ruled is an intolerable and insidious contrast, yet the resulting hatred is much the same. The insidiousness of this situation is illustrated earlier in Orwell's essay as he mentions "[T]he wretched prisoners huddling in the stinking cages of the lockups" which make him feel guilty while at the same time he thinks that "the greatest joy in the world would be to drive a bayonet into a Buddhist priest's guts" because they appear to have nothing to do but look resentfully and jeer at Europeans from street corners.

Furthermore, the incident of Orwell's shooting of the rogue elephant becomes metaphoric for the violence that the roles of ruler and ruled portend. In his criticism, "Understanding 'Shooting an Elephant' in an Anthropological and Non-Political Way," Thomas Bertonneau comments,

If the British presence, enforcing itself by violence against the Burmese, is unjust, violating the intuitive rules of universal humanity, then the Burmese persecution of individual Europeans is no less unjust according to the same criterion.

In other words, cruelty exists both in the oppressor and in the oppressed. Certainly, the imprisonment and the flogging of the Burmese is cruel, but so also are the Burmese's random acts of Orwell's being tripped in a soccer game and the insults "hooted" at him as the crowd "yelled with hideous laughter," the spitting of betel juice upon the dress of a European woman, and the crowd's following Orwell with "faces all happy and excited over this bit of fun" pressuring him into killing the elephant to avoid appearing foolish before them. Thus, ironically perhaps, the ruled cruelly force actions upon the rulers later after the rulers have acted in a cruel manner toward them. 

Therefore, the role of the ruler is to maintain domination of the conquered. Orwell shoots the rogue elephant because the Burmese expect him to do so; not shooting it would be perceived as weakness, so Orwell feels as an officer of the law that he has no other option, unless he wants to look like a fool. On the other hand, the ruled Burmese feel a invidious resentment toward the ruling people; this intolerance on their part leads to anger and violence. Thus, the ruled try to undermine the authority of the ruler(s) and cause the ruler to lose strength and eventually the stronghold upon them. According to the oppressor, the role of the ruled is to remain in the dominate position of control; however for others, the role of the ruled is to jeopardize the dominant position of the ruled in any way they can.