As I continue to think further about influence and power, Howard Gardner's Changing Minds offers an extremely helpful conceptual framework, one that I see as a counterpart to Robert Cialdini's "Weapons of Influence" (discussed at length in Cialdini's Influence: The Psychology of Persuasion.) From Gardner's 2006 edition:
[W]hat...factors might cause an individual to shift his or her perspective[?]... I have identified seven factors--sometimes I'll call them levers--that could be at work in these and all cases of a change of mind...
A rational approach involves identifying of relevant factors, weighing each in turn, and making an overall assessment. Reason can involve sheer logic, the use of analogies, or the creation of taxonomies.
Complementing the use of argument is the collection of relevant data... But research need not be formal; it need only entail the identification of relevant cases and a judgment about whether they warrant a change of mind.
Reason and research appeal to the cognitive aspects of the human mind; resonance denotes the affective component. A view, idea or perspective resonates to the extent that it feels right to an individual, seems to fit the current situation, and convinces the person that further considerations are superfluous.
Representational Redescriptions (Redescriptions, for Short)
A change of mind becomes convincing to the extent that it lends itself to representation in a number of different forms, with these forms reinforcing each other... Particularly when it comes to matters of instruction...the potential for expressing the desired lesson in many compatible formats is crucial.
Resources and Rewards
[T]he provision of resources is an instance of positive reinforcement... Individuals are being rewarded for one course of behavior and thought rather than another. Ultimately, however, unless the new course of thought is concordant with other criteria...it is unlikely to last beyond the provision of resources.
Real World Events
Sometimes an event occurs in the broader society that affects many individuals, not just those who are contemplating a mind change. Examples are wars, hurricanes, terrorist attaches, economic depressions--or, on a more positive side, eras of peace and prosperity...
[W]e develop strong view and perspectives that are resistant to change... [A] mind change is most likely to come about when the first six factors operate in consort and the resistances are relatively weak.
Taken together, Gardner's "seven levers" and Cialdini's "six weapons" form a reasonably comprehensive conceptual model of influence--the central "layer" in my Influence Pyramid. If these models are our starting point for understanding not just how influence works but also how we as individuals can be more influential, we can then move "down" the pyramid to consider 1) our self-awareness and our impact on others and 2) our internal beliefs about power, or "up" the pyramid to 3) translate these strategic concepts into tactical tools and 4) test them empirically.
Note that by focusing on Cialdini and Gardner, I don't mean to imply that their conceptual models are the only ones worth studying, but they're the most compelling ones I've encountered to date. (And to Gardner's comments on redescriptions above, they also both translate well into different formats--in that regard, they're even more...influential.)