A tendency to impact, control or influence someone is known as power. A dictionary definition of power would include control or influence in its explanation.
Power is virtually self defining and allows someone or an organization to exert influence over others. A government, local authority or police force is an obvious example of a body that exerts power over others. Although there is no outward show of control or influence, the very presence of police or government provides a subtle sign of power which although largely irrelevant to most people does influence others who would act differently if there was no signs of control over their behavior.
Influence is a more subtle form of power. By creating an influence it impacts on how someone behaves or reacts without having to be assertive. Influences can be for good or bad and provide an example without going as far as to suggest a role model. The more subtle an influence is the more successful it will be. Where something is obvious or blatant it will be less influential
Achievement can be a mix of power or influence and can set an example. Achievement is something that people can look up to, to admire and emulate and is more obvious than influencing. Achievement can come in an academic or personal field and is something that is measured and tested to have provided success.
While the other answers offered to this question have some merit, the power answer provides the best fix on a number of grounds. Affiliation and achievement will be a part of power but only the power answer covers the key elements of the question such as impact, control and influence.
