Scale-free interpersonal influences on opinions in complex systems

An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less vigorous on small differences of opinion than large differences. Opinion differences that may be measured on the real number line may not directly correspond to the subjective importance of an issue and extent of resistance to opinion change. This is a hard problem for field of opinion dynamics, a field that has become increasingly prominent as it has attracted more contributions to it from investigators in the natural and engineering sciences. The paper contributes a scale-free approach to assessing the extents to which individuals, with unknown heterogeneous resistances to influence, have been influenced by the opinions of others.