The network of weighted majority rules and its geometric realizations

Abstract In a previous work the first author considered the network G ( n , p ) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p =( p 1 ,…, p n ) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G ( n , p ) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.