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We consider a general class of three--state models where individuals hold oneof two opposite opinions, or are neutral, and exchange opinions in genericpairwise interactions. We show that when opinions spread in a population wherea fraction of individuals (zealots) maintain unshakably their opinion, one offour qualitatively distinct kinds of collective dynamics arise, depending onthe specific rules governing the social interactions. Unsurprisingly, whentheir density is high, zealots drive the whole population to consensus on theiropinion. For low densities a rich phase diagram emerges: a finite population ofdissenters can survive and be the only stationary state or may need a criticalmass or dissenters to be sustained; the critical mass may vanish or not as thedensity is reduced; the transition to the high density regime can be smooth orabrupt, and shows interesting hysteretic effects. For each choice of theinteraction rules we calculate the critical density of zealots above whichdiverse opinions cannot survive.

Consensus versus persistence of disagreement in opinion formation: the role of zealots