Rational debate and one-dimensional conflict

This paper studies repeated communication regarding a multidimensional collective decision in a large population. When preferences coincide but beliefs about the consequences of the various decisions diverge, it is shown, under some specific assumptions, that public communication causes the disagreement between beliefs either to vanish or to become one-dimensional at the limit. Multidimensional disagreement indeed allows for many directions of communication, including some that are orthogonal to the conflict, along which agents can communicate credibly. The possible convergence toward a one-dimensional conflict where no further communication takes place may be related to the empirically observed geometry of the political conflict in many countries.