In this study we present a new analytical model of a Parliament and investigate the beneficial effects of the selection of legislators by lot in order to reduce some of the drawbacks of modern representative democracies. Resorting to sortition for the selection of public officers used to be in the past a popular way of taming factionalism in public affairs. Factionalism is assumed to be detrimental since public officers tend to favour their own faction instead of pursuing the general interest. In this respect our mathematical model shows in a rigorous way how it is possible to improve the efficiency of a Parliament by introducing the use of sortition to select part of its members. It will be shown that, starting from a Parliament working with two parties (or coalitions), where the costs of representative democracy are quite apparent through the detrimental effects of party discipline, one can beneficially move towards a Parliament where independent, randomly selected legislators sit alongside elected members. In particular, we show that increasing the number of independent legislators up to a critical point enhances the efficiency of the Parliament and puts into check the factionalism likely to arise from party discipline.
