  There is growing evidence of systematic attempts to influence democratic
elections by controlled and digitally organized dissemination of fake news.
This raises the question of the intrinsic robustness of democratic electoral
processes against external influences. Particularly interesting is to identify
the social characteristics of a voter population that renders it more resilient
against opinion manipulation. Equally important is to determine which of the
existing democratic electoral systems is more robust to external influences.
Here we construct a mathematical electoral model to address these two
questions. We find that, not unexpectedly, biased electorates with clear-cut
elections are overall quite resilient against opinion manipulations, because
inverting the election outcome requires to change the opinion of many voters.
More interesting are unbiased or weakly biased electorates with close
elections. We find that such populations are more resilient against opinion
manipulations (i) if they are less polarized and (ii) when voters interact more
with each other, regardless of their opinion differences, and that (iii)
electoral systems based on proportional representation are generally the most
robust. Our model qualitatively captures the volatility of the US House of
Representatives elections. We take this as a solid validation of our approach.
