  Asymmetry in contrarian behavior is investigated within the Galam model of
opinion dynamics using update groups of size 3 with two competing opinions A
and B. Denoting $x$ and $y$ the respective proportions of A and B contrarians,
four schemes of implementations are studied. First scheme activates contrarians
after each series of updates with probabilities $x$ and $y$ for agents holding
respectively opinion A and B. Second scheme activates contrarians within the
update groups only against global majority with probability $x$ when A is
majority and $y$ when B is majority. Third scheme considers in-group
contrarians acting prior to the local majority update against both local
majority and minority opinions. Last scheme activates in-group contrarians
prior to the local majority update but only against the local majority. The
main result is the loss of the fifty-fifty attractor produced by symmetric
contrarians. Producing a bit less contrarians on its own side than the other
side becomes the key to win a public debate, which in turn can guarantee an
election victory. The associated phase diagram of opinion dynamics is found to
exhibit a rich variety of counterintuitive results.
