Vulnerabilities of democratic electoral systems

Trabajo presentado en la Conference on Complex Systems (CCS), celebrada en Lyon del 25 al 29 de octubre de 2021.The vulnerability of democratic processes is under scrutiny after scandals related to Cambrige Analytica (2016 U.S. elections, the Brexit referendum, and elections in Kenya [1]). The deceptive use of social media in the US, the European Union and several Asian countries, increased social and political polarization across world regions. Finally, there are straightforward frauds like Crimea referendum and Belarus elections. These challenges are eroding democracy, the most frequent source of governmental power, and raise multiple questions about its vulnerabilities [2]. Democratic systems have countless ways of performing elections, which create different electoral systems (ES). It is therefore in citizens’ interest to study and understand how different ESs relate to different vulnerabilities and contemporary challenges. These systems can be analyzed using network science in various layers – they involve a network of voters in the first place, a network of electoral districts connected by commuting flow for instance, or a network of political parties to give a few examples. The electoral system together with the underlying voting processes and opinion dynamics can be seen as a complex system [3]. We study electoral systems in a dynamical framework. We look at the volatility of the election results, analyzing how much they vary over time. However, the term volatility is frequently used in relation to the Pedersen index of volatility. In this meaning it has been studied and even linked to the party system instability [4, 5]. Our approach goes far beyond two-point volatility. We analyze the vulnerability of an ES based on a long run of opinion dynamics process with many elections performed during the evolution. In this context, we consider that a system is more vulnerable, if it has a larger variance of the election results and if it magnifies the influence of extremism and media. We can further identify which voting system is more sensitive to fluctuations, and which one is more vulnerable to internal/external influences, like zealots or propaganda. This allows us to construct a probability distribution of election results under every electoral system. It is essential to provide new tools and arguments to the discussion on the evaluation of electoral systems. We aim at comparing different ESs in a dynamical framework. Our novel approach of analyzing electoral systems in such way with all its aspects included, from opinion dynamics in the population of voters to inter-district commuting patterns to seat appointment methods, will help answering questions like: Which electoral systems are more predictable/stable under fluctuations? Which electoral systems are the most robust (or vulnerable) under external and internal influences? Which features of electoral systems make them more (less) stable