A national voting population, when segmented into groups such as, for example, different states, can yield a counterintuitive scenario in which the winner may not necessarily get the highest number of total votes. A recent example is the 2016 presidential election in the United States. We model the situation by using interacting opinion dynamics models, and we 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 take all” electoral college system in the United States, can give rise to finite probabilities of events in which a minority candidate wins 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 indicate that one may expect more instances of minority candidate winning in the future.