Critical states in Political Trends. How much reliable is a poll on Twitter? A study by means of the Potts Model
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In recent years, Twitter data related to political trends have tentatively been used to make predictions (poll) about several electoral events. Given q candidates for an election and a time-series of Twitts (short messages), one can extract the q mean trends and the q(q+1)/2 Twitt-to-Twitt correlations, and look for the statistical models that reproduce these data. On the base of several electoral events and assuming a stationary regime, we find out the following: i) the maximization of the entropy singles out a microscopic model (single-Twitt-level) that coincides with a q-state Potts model having suitable couplings and external fields to be determined via an inverse problem from the two sets of data; ii) correlations decay as 1/N_eff, where N_eff is a small fraction of the mean number of Twitts; iii) the simplest statistical models that reproduce these correlations are the multinomial distribution (MD), characterized by q external fields, and the mean-field Potts model (MFP), characterized by one coupling; iv) remarkably, this coupling turns out to be always close to its critical value. This results in a MD or MFP model scenario that discriminates between cases in which polls are reliable and not reliable, respectively. More precisely, predictions based on polls should be avoided whenever the data maps to a MFP because anomalous large fluctuations (if q=2) or sudden jumps (if q≥ 3) in the trends might take place as a result of a second-order or a first-order phase transition of the MFP, respectively.
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