Representativeness of the parties and the Bundestag

This is the first out of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections by the methods of the mathematical theory of democracy. This one estimates the policy representation ability of the 39 parties that participated in the 2021 elections and the Bundestag. For this purpose, the positions of the parties on 38 topical issues are compared with the results of recent public opinion polls. Then the parties' indices of popularity (the average percentage of the population represented) and universality (frequency in representing a majority) are constructed. Assuming that the Bundestag's position on the 38 issues is determined by the Bundestag majority, the Bundestag's indices of popularity and universality are estimated as well. The main conclusion is that the representativeness of the Bundestag parties and the Bundestag (before coalition-formation) has significantly increased since 2017. In particular, the election winner, the SPD, is now ranked 4 instead of 22 in 2017, having the mean index (popularity + universality) / 2 = 65% instead of 52 % in 2017. The Bundestag's mean index is now equal to 61% instead of former 40%. As for the ruling 'Traffic light coalition', SPD+GRUNE+FDP, its compatibility is as low as 45% and the representativeness is not the best either.