  In this paper, we discuss the possible generalizations of the Social
Influence with Recurrent Mobility (SIRM) model developed in Phys. Rev. Lett.
112, 158701 (2014). Although the SIRM model worked approximately satisfying
when US election was modelled, it has its limits: it has been developed only
for two-party systems and can lead to unphysical behaviour when one of the
parties has extreme vote share close to 0 or 1. We propose here generalizations
to the SIRM model by its extension for multi-party systems that are
mathematically well-posed in case of extreme vote shares, too, by handling the
noise term in a different way. In addition, we show that our method opens new
applications for the study of elections by using a new calibration procedure,
and makes possible to analyse the influence of the "free will" (creating a new
party) and other local effects for different commuting network topologies.
