  Opinion diffusion is a crucial phenomenon in social networks, often
underlying the way in which a collective of agents develops a consensus on
relevant decisions. The voter model is a well-known theoretical model to study
opinion spreading in social networks and structured populations. Its simplest
version assumes that an updating agent will adopt the opinion of a neighboring
agent chosen at random. The model allows us to study, for example, the
probability that a certain opinion will fixate into a consensus opinion, as
well as the expected time it takes for a consensus opinion to emerge.
  Standard voter models are oblivious to the opinions held by the agents
involved in the opinion adoption process. We propose and study a
context-dependent opinion spreading process on an arbitrary social graph, in
which the probability that an agent abandons opinion $a$ in favor of opinion
$b$ depends on both $a$ and $b$. We discuss the relations of the model with
existing voter models and then derive theoretical results for both the fixation
probability and the expected consensus time for two opinions, for both the
synchronous and the asynchronous update models.
