Modelling Responsiveness in Legislative Deliberation: A Graph-theoretic Approach to Rebuttal Identification and Quality Assessment

Abstract The quality of parliamentary debate is foundational to democratic legitimacy, yet empirical assessments of deliberation often remain anchored in manual content analysis or broad-brush sentiment metrics. These approaches, while valuable, frequently overlook the structural dimension of discourse — specifically, the degree to which legislators substantively respond to one another rather than delivering isolated, pre-scripted monologues. This paper introduces a novel graph-theoretic framework for modelling legislative responsiveness. By parsing digital parliamentary records, we construct directed debate networks in which nodes represent individual speech turns and edges denote explicit or implicit rebuttal links identified through a hybrid pipeline combining speaker cue detection, semantic contrast scoring, and graph-constrained validation. Moving beyond simple adjacency, we derive a set of structural metrics — including network reciprocity, transitivity, and weighted clustering coefficients — to serve as quantifiable proxies for the integrity and depth of deliberation. We validate this approach against a longitudinal corpus of 1,200 plenary sessions, examining how rebuttal-graph topology correlates with legislative productivity and partisan polarisation. High-reciprocity, densely inter-factional networks predict substantially greater legislative output, even in polarised environments. This research contributes a scalable, language-agnostic methodology for evaluating parliamentary discourse, offering political scientists and democratic watchdogs a robust new instrument for measuring deliberative responsiveness in the digital age.