  Large-scale data from social media have a significant potential to describe
complex phenomena in real world and to anticipate collective behaviors such as
information spreading and social trends. One specific case of study is
represented by the collective attention to the action of political parties. Not
surprisingly, researchers and stakeholders tried to correlate parties' presence
on social media with their performances in elections. Despite the many efforts,
results are still inconclusive since this kind of data is often very noisy and
significant signals could be covered by (largely unknown) statistical
fluctuations. In this paper we consider the number of tweets (tweet volume) of
a party as a proxy of collective attention to the party, identify the dynamics
of the volume, and show that this quantity has some information on the
elections outcome. We find that the distribution of the tweet volume for each
party follows a log-normal distribution with a positive autocorrelation of the
volume over short terms, which indicates the volume has large fluctuations of
the log-normal distribution yet with a short-term tendency. Furthermore, by
measuring the ratio of two consecutive daily tweet volumes, we find that the
evolution of the daily volume of a party can be described by means of a
geometric Brownian motion (i.e., the logarithm of the volume moves randomly
with a trend). Finally, we determine the optimal period of averaging tweet
volume for reducing fluctuations and extracting short-term tendencies. We
conclude that the tweet volume is a good indicator of parties' success in the
elections when considered over an optimal time window. Our study identifies the
statistical nature of collective attention to political issues and sheds light
on how to model the dynamics of collective attention in social media.
