Measuring Political Polarization: Twitter shows the two sides of Venezuela

We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin by proposing a model to estimate opinions in which a minority of influential individuals propagate their opinions through a social network. The result of the model is an opinion probability density function. Next, we propose an index to quantify the extent to which the resulting distribution is polarized. Finally, we apply the proposed methodology to a Twitter conversation about the late Venezuelan president, Hugo Ch\'avez, finding a good agreement between our results and offline data. Hence, we show that our methodology can detect different degrees of polarization, depending on the structure of the network.