A model to support collective reasoning: Formalization, analysis and
  computational assessment
  Inspired by e-participation systems, in this paper we propose a new model to
represent human debates and methods to obtain collective conclusions from them.
This model overcomes drawbacks of existing approaches by allowing users to
introduce new pieces of information into the discussion, to relate them to
existing pieces, and also to express their opinion on the pieces proposed by
other users. In addition, our model does not assume that users' opinions are
rational in order to extract information from it, an assumption that
significantly limits current approaches. Instead, we define a weaker notion of
rationality that characterises coherent opinions, and we consider different
scenarios based on the coherence of individual opinions and the level of
consensus that users have on the debate structure. Considering these two
factors, we analyse the outcomes of different opinion aggregation functions
that compute a collective decision based on the individual opinions and the
debate structure. In particular, we demonstrate that aggregated opinions can be
coherent even if there is a lack of consensus and individual opinions are not
coherent. We conclude our analysis with a computational evaluation
demonstrating that collective opinions can be computed efficiently for
real-sized debates.
