  The two most common types of electoral systems (ES) used in electing national
legislatures are proportional representation and plurality voting. When they
are evaluated, most often the arguments come from social choice theory and
political sciences. The former overall uses an axiomatic approach including a
list of mathematical criteria a system should fulfill. The latter predominantly
focuses on the trade-off between proportionality of apportionment and
governability. However, there is no consensus on the best ES, nor on the set of
indexes and measures that would be the most important in such assessment.
Moreover, the ongoing debate about the fairness of national elections neglects
the study of their vulnerabilities. Here we address this research gap with a
framework that can measure electoral systems' vulnerability to different means
of influence. Using in silico analysis we show that plurality voting systems
are less stable than proportional representation. They are also more
susceptible to political agitators and media propaganda. A review of real-world
ES reveals possible improvements in their design leading to lower
susceptibility. Additionally, our simulation framework allows computation of
popular indexes, as the Gallagher index or the effective number of parties, in
different scenarios. Our work provides a new tool for dealing with modern
threats to democracy that could destabilize voting processes. Furthermore, our
results add an important argument in a long-standing discussion on evaluation
of ES.
