A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

According to the penalty hypothesis, primaries are considered damaging for parties because of the social and political distinctiveness of the electorate, who usually choose unpalatable candidates for the median voter in general elections. This article deals with two leader selections organised by the Italian Partito Democratico (PD) in 2007 and 2009. Using survey data, voters' characteristics in the two primaries relating to the 2008 parliamentary elections are contrasted in order to find out the differences between the two selectorates and the general electorate. Then, the attitudes of the winners' and losers' supporters in primary elections are compared. Although not definitive, the results contradict the primary penalty thesis. Even if the data point out some relevant differences between selectors and electors, the losers' supporters do not seem to be demobilised by the primary results.