Contrarian Deterministic Effect: the "Hung Elections Scenario"

A contrarian is someone who deliberately decides to oppoe the prevailing choice of others. The Galam model of two state opinion dynamicsincorporates agent updates by a single step random grouping in which all participants adopt the opinion of their respective local majority group. The process is repeated until a stable collective state is reached; the associated dynamics is fast. Here we show that the introduction of contrarians may give rise to interesting dynamics generated phases and even to a critical behavior at a contrarian concentration $a_c$. For $a<a_c$ an ordered phase is generated with a clear cut majority-minority splitting. By contrast when $a>a_c$ the resulting disordered phase has no majority: agents keep shifting opinions but no symmetry breaking (i.e., the appearance of a majority) takes place. Our results are employed to explain the outcome of the 2000 American presidential elections and that of the 2002 German parliamentary elections. Those events are found to be inevitable. On this basis the ``hung elections scenario'' is predicted to become a common occurrence in modern democracies.