  Social contagion has been studied in various contexts. Many instances of
social contagion can be modeled as an infection process where a specific state
(adoption of product, fad, knowledge, behavior, etc.) spreads from individual
to individual through links between them. In the meantime, other forms of
social contagion may better be understood as a diffusion process where the
state of an individual tends to assimilate with the social norm (i.e., local
average state) within his/her neighborhood.
  Unlike infection scenarios where influence is nonlinear, unidirectional,
fast, and potentially disruptive, social diffusion is linear, bidirectional,
gradual, and converging. The distance between an individual's state and his/her
neighbors' average state always decreases, and thus a homogeneous global state
is guaranteed to be the network's stable equilibrium state in the long run.
This does not sound as intriguing or exciting as infection dynamics, which
might be why there are very few studies on mathematical models of social
diffusion processes.
  Here, this study attempts to shed new light on an unrecognized characteristic
of social diffusion, i.e., non-trivial drift it can cause to the network's
global average state. Although somewhat counterintuitive, such global drift is
indeed possible because, unlike physical diffusion processes, social diffusion
processes are not conservational. In what follows, a mathematical model of
social diffusion will be presented to explain the mechanism of this phenomenon,
and some possible collective actions for influencing the direction of global
drift will be proposed. The relevance of social diffusion to individual and
collective improvement will be discussed briefly, with an emphasis on
educational applications.
