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

## TL;DR

This study uses a statistical physics approach, specifically the Potts Model, to evaluate the reliability of Twitter-based political polls by analyzing correlations and phase transitions in tweet data.

## Contribution

It introduces a novel inverse modeling method linking Twitter data to a Potts Model, revealing critical points that determine poll reliability.

## Key findings

- Correlations decay as 1/N_eff, with N_eff being a small fraction of total tweets.
- Simple models like multinomial and mean-field Potts can reproduce observed correlations.
- Couplings in the model are close to critical values, indicating potential phase transitions affecting poll reliability.

## Abstract

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 $q\geq 3$) in the trends might take place as a result of a second-order or a first-order phase transition of the MFP, respectively.