Abstract
Political elections exemplify complex decision processes in human populations. Data of proportional elections show a striking feature at different spatial scales, across years, and for several democracies: when ranking the parties according to their number of voters, the amount of votes grows exponentially with the party’s rank. We develop a mechanistic mathematical model of birth and death of parties and voter grouping based only on word of mouth and not on political contents, close to neutral models used in evolutionary biology (Ewens sampling formula), or Hubbell’s model of species biodiversity. Data and model agree strikingly well. The model explains, for instance, the steady loss of big-tent parties in France and Germany by the increasing number of parties standing for elections. A cannibalism effect (parties/candidates at a given rank systematically withdraw votes from others) can be identified. The interpretation and consequences of the rational or lack thereof of voters’ choices for modern democracies are discussed.
Highlights
Elections are at the heart of modern democracies
We find this relationship in proportional elections in Germany since 1949, the first round of presidential elections in France (2005, 2012 and 2017), recent elections in the Netherlands (1972–2017), and the Republican primaries in the United States of America (USA) (2016) (Fig. 1a–d and Supplementary Information (SI) Figures)
At several spatial scale hints to an underlying dynamical process that seems to be incompatible with our idea of elections
Summary
Elections are at the heart of modern democracies. In our understanding of elections, mature citizens consider the challenges the society is faced with, and decide rationally about the best approach for the coming years. Perhaps the most striking finding in these studies is that the double logarithmic plot appears to be linear, indicating a power law relation In contrast to these papers, we investigate proportional elections with only few candidates/parties, where each candidate/ party represents a different choice. This observation indicates an exponential growth of the number of voters with the rank of the parties We find this relationship in proportional elections in Germany since 1949, the first round of presidential elections in France (2005, 2012 and 2017), recent elections in the Netherlands (1972–2017), and the Republican primaries in the USA (2016) (Fig. 1a–d and Supplementary Information (SI) Figures). In view of recent developments in western democracies it is necessary to identify the underlying mechanisms and to give appropriate interpretations of these observations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
