A penalized inference approach to stochastic blockmodelling of community structure in the Italian Parliament

In many parliamentary systems, bills can be proposed by a single parliamentarian, or cosponsored by a group of parliamentarians. In the latter case, bill cosponsorship defines a symmetric relation that can be taken as a measure of ideological agreement between parliamentarians. Political scientists have analysed bill cosponsorship networks in the Congress of the USA, assessing its community structure and the behaviour of minorities therein. In this paper we analyse bill cosponsorship in the Italian Chamber of Deputies from 2001 to 2015. Compared to the US Congress, a distinguishing feature of the Italian Chamber is the presence of a large number of political groups: the primary purpose of the analysis is thus to infer the pattern of collaborations between these groups. We consider a stochastic blockmodel for edge-valued graphs that views bill cosponsorship as the result of a Poisson process, and derive measures of group relevance and preferential attachment between political parties. As the number of model parameters increases quickly with the number of groups, we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph, which summarizes collaborations between political parties. ∗[email protected] 1 ar X iv :1 60 7. 08 74 3v 1 [ st at .A P] 2 9 Ju l 2 01 6 Besides showing the effects of gender and geographic proximity on bill cosponsorship, the analysis points out the evolution from a highly polarized political arena, in which deputies base collaborations on their identification with left or right-wing values, towards an increasingly fragmented Parliament, where a rigid separation of political groups into coalitions does not hold any more, and collaborations beyond the perimeter of coalitions have become possible.