  The combined effects of collective beliefs and individual stubbornness in the
dynamic of a public debate are investigated using the Galam sequential
probabilistic model of opinion dynamics. The study is focused on pair
interactions for which the bias produced by collective beliefs is the decisive
factor to win the debate. The current value of that bias is a fixed external
parameter. It is a constant of the problem not given to change. In contrast,
stubbornness is an individual property. It results from external ingredients,
which are susceptible to be modified during the debate. More precisely, giving
some beliefs we determine the required stubbornness to oppose its associated
bias in the debate outcome. The results shed a new and counter intuitive light
on paradoxical outcomes of sensitive issues, which are discussed in the public.
The case of the global warming issue is discussed.
