It sometimes seems as though there is a normative dimension to our concept of power. What if we defined "power" in these terms: an agent exercises power when he/she undertakes to compel individuals or groups to act in ways they prefer not to act, against their interests and without the justification of a legitimate state underwriting the compulsion. Notice that the last qualification entails that the exercise of power is by definition "illegitimate"; legitimate authority compels behavior but does not exercise power. So on this definition, there is a behavioral element and a normative element in the proposition that "A exercises power over B": A compels behavior by B and A does not have a legitimate political or moral right to do so.
This might appear to be largely a semantic question: what do we mean by "power"? Is the exercise of the enforcement of law within a procedurally and substantively just polity an exercise of "power"? Or is it rather the exercise of rightful authority?
Certainly it is correct to observe that the behavioral aspect of involuntary compulsion is present in both types of cases. The criminal who is imprisoned for his crimes is treated coercively, in that he is confined against his will; so the state has the ability to "compel individuals to act contrary to their will". If we took the element of compulsion and coercion as uniquely central, then both the lawful state and the extortion gang are exercising power -- over criminals and innocent citizens respectively. If, on the other hand, we think that coercively backed authority is something different from "power", then a democratically established legal authority cannot be said to be exercising power over its citizens (though it may do so over its international adversaries).
If we go down this road in analyzing power, then there is a close relationship between power, social justice, and democracy.
How would we decide this question? And does it have any importance for the purposes of social and political explanation, or for the design of social policies?