Contrarian deterministic effects on opinion dynamics: the hung elections scenario

We study the effects of contrarians on the dynamics of opinion forming using the 2-state Galam opinion dynamics model. In a single update step, groups of a given size are defined and all agents in each group adopt the state of the local majority. In the absence of contrarians, the dynamics is fast and leads to a total polarization always along the initial majority (for groups of odd sizes). The introduction of contrarians is then shown to give rise to interesting new dynamics properties. First, at low concentration a, a new mixed phase is stabilized with a coexistence of both states. This is an ordered phase with a clear cut majority-minority splitting (non zero order parameter). Second, there is a phase transition into a new disordered phase at a(c)=1/6, 0.23, 0.30...1/2 for groups of respective sizes 3, 5, 9 and infinite. For agreater than or equal toa(c) the disordered phase has no opinion dominating with both state densities equal (zero order parameter). In this phase agents keep shifting states but no global symmetry breaking, i.e., the appearance of a majority, takes place. Our results may shed a new light on the phenomenon of hung elections as occured in the 2000 American presidential elections and that of the 2002 German parliamentary elections. (C) 2003 Elsevier B.V. All rights reserved.