We study a prototypical model of a Parliament with two Parties or two
Political Coalitions and we show how the introduction of a variable percentage
of randomly selected independent legislators can increase the global efficiency
of a Legislature, in terms of both the number of laws passed and the average
social welfare obtained. We also analytically find an "efficiency golden rule"
which allows to fix the optimal number of legislators to be selected at random
after that regular elections have established the relative proportion of the
two Parties or Coalitions. These results are in line with both the ancient
Greek democratic system and the recent discovery that the adoption of random
strategies can improve the efficiency of hierarchical organizations.Comment: 19 pages, 7 figures, new improved and longer versio