  Inspired by the spread of discontent as in the 2016 presidential election, we
consider a voter model in which 0's are ordinary voters and 1's are zealots.
Thinking of a social network, but desiring the simplicity of an infinite object
that can have a nontrivial stationary distribution, space is represented by a
tree. The dynamics are a variant of the biased voter: if $x$ has degree $d(x)$
then at rate $d(x)p_k$ the individual at $x$ consults $k\ge 1$ neighbors. If at
least one neighbor is 1, they adopt state 1, otherwise they become 0. In
addition at rate $p_0$ individuals with opinion 1 change to 0. As in the
contact process on trees, we are interested in determining when the zealots
survive and when they will survive locally.
