  We consider the median dynamics process in general graphs. In this model,
each vertex has an independent initial opinion uniformly distributed in the
interval [0,1] and, with rate one, updates its opinion to coincide with the
median of its neighbors. This process provides a continuous analog of binary
majority dynamics. We deduce properties of median dynamics through this
connection and raise new conjectures regarding the behavior of majority
dynamics on general graphs. We also prove these conjectures on some graphs
where majority dynamics has a simple description.

Probability;Discrete Mathematics