3 December 2009, Computational Social Choice Seminar, Daniele Porello
Arrow's theorem shows a tension between democratic desiderata of preference aggregation procedures and rationality constraints on preference orderings. One well-known solution to avoid such problems is to restrict the domain of the aggregation procedure to some well-behaved class of profiles of individual preferences. In particular, Black's condition of single-peakedness assures consistent collective outcomes and is particularly interesting for its convincing intuitive interpretation: it means that individual preferences share a common dimension of voting. The process of reaching a shared dimension has been investigated in the literature (e.g., Dryzeck and List 2003) and it has been considered as an effect of deliberation. I will propose some remarks on what happens when a shared dimension already exists.
Firstly, I will stress that a verbalization of the existing dimension is required in order to model discussion or voting on dimensions. Then, I will sketch a model to state the relationship between preferences and verbalization of dimensions, seen as public justifications of preference orderings. I will presents some results, that hold for single-peaked profiles, showing that even if preference aggregation is safe, the deliberation concerning public justifications leads to inconsistencies known as discursive dilemmas.
J.S. Dryzeck and C. List, 2003, "Social Choice Theory and Deliberative Democracy: A Reconciliation", British Journal of Political Science, 33: 1-28.