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In recent years, Twitter data related to political trends have tentativelybeen used to make predictions (poll) about several electoral events. Given $q$candidates for an election and a time-series of Twitts (short messages), onecan 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 ofseveral electoral events and assuming a stationary regime, we find out thefollowing: i) the maximization of the entropy singles out a microscopic model(single-Twitt-level) that coincides with a $q$-state Potts model havingsuitable couplings and external fields to be determined via an inverse problemfrom 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 simpleststatistical models that reproduce these correlations are the multinomialdistribution (MD), characterized by $q$ external fields, and the mean-fieldPotts model (MFP), characterized by one coupling; iv) remarkably, this couplingturns out to be always close to its critical value. This results in a MD or MFPmodel scenario that discriminates between cases in which polls are reliable andnot reliable, respectively. More precisely, predictions based on polls shouldbe avoided whenever the data maps to a MFP because anomalous large fluctuations(if $q=2$) or sudden jumps (if $q\geq 3$) in the trends might take place as aresult of a second-order or a first-order phase transition of the MFP,respectively.

Critical states in Political Trends. How much reliable is a poll on Twitter? A study by means of the Potts Model