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Data of proportional elections show a striking feature: If the parties areranked according to the number of their voters, the number of votes growsexponentially with the rank of the party. This so-called Zipf's law has beenreported before. We first show this correlation in results from recentelections in Germany, France and republican primaries in the USA. However themechanism generating such feature remains so far unexplained. We develop amathematical model of voter grouping that is only based on the word of mouthand not on political contents. The model is close to the infinite allele modeland the Ewens sampling formula that are well known in population genetics.Strikingly, the model generates output agreeing very well with the observedelection data. We further identify a cannibalism effect in Germany, wherebyparties above the 5% threshold withdraw votes from parties just below thethreshold. We demonstrate that the number of parties present in the parliamentcan be predicted given the number of parties standing for election. Finally,the steady loss of big-tent parties in Germany in the last 20 years relates tothe increasing number of parties since 1975. We discuss the interpretation andconsequences of these findings for modern democracies and the rationality orlack thereof of voters' choices.

Do voters choose rationally, irrationally or at random? Data and theory for proportional elections