  A national voting population, when segmented into groups like, for example,
different states, can yield a counter-intuitive scenario where the winner may
not necessarily get the most number of total votes. A recent example is the
2016 presidential election in the US. We model the situation by using
interacting opinion dynamics models and look at the effect of coarse graining
near the critical points where the spatial fluctuations are high. We establish
that the sole effect of coarse graining, which mimics the `winner takes all'
electoral college system in the US, can give rise to finite probabilities of
such events of minority candidate winning even in the large size limit near the
critical point. The overall probabilities of victory of the minority candidate
can be predicted from the models which indicates that one may expect more
instances of minority candidate winning in the future.
