  Data of proportional elections show a striking feature: If the parties are
ranked according to the number of their voters, the number of votes grows
exponentially with the rank of the party. This so-called Zipf's law has been
reported before. We first show this correlation in results from recent
elections in Germany, France and republican primaries in the USA. However the
mechanism generating such feature remains so far unexplained. We develop a
mathematical model of voter grouping that is only based on the word of mouth
and not on political contents. The model is close to the infinite allele model
and the Ewens sampling formula that are well known in population genetics.
Strikingly, the model generates output agreeing very well with the observed
election data. We further identify a cannibalism effect in Germany, whereby
parties above the 5% threshold withdraw votes from parties just below the
threshold. We demonstrate that the number of parties present in the parliament
can 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 to
the increasing number of parties since 1975. We discuss the interpretation and
consequences of these findings for modern democracies and the rationality or
lack thereof of voters' choices.
