  We consider opinion diffusion for undirected networks with sequential updates
when the opinions of the agents are single-peaked preference rankings. Our
starting point is the study of preserving single-peakedness. We identify voting
rules that, when given a single-peaked profile, output at least one ranking
that is single peaked w.r.t. a single-peaked axis of the input. For such voting
rules we show convergence to a stable state of the diffusion process that uses
the voting rule as the agents' update rule. Further, we establish an efficient
algorithm that maximises the spread of extreme opinions.
