  The electoral college of voting system for the US presidential election is
analogous to a coarse graining procedure commonly used to study phase
transitions in physical systems. In a recent paper, opinion dynamics models
manifesting a phase transition, were shown to be able to explain the cases when
a candidate winning more number of popular votes could still lose the general
election on the basis of the electoral college system. We explore the
dependence of such possibilities on various factors like the number of states
and total population (i.e., system sizes) and get an interesting scaling
behavior. In comparison with the real data, it is shown that the probability of
the minority win, calculated within the model assumptions, is indeed near the
highest possible value. In addition, we also implement a two step coarse
graining procedure, relevant for both opinion dynamics and information theory.
