  We study the minority-opinion dynamics over a fully-connected network of $n$
nodes with binary opinions. Upon activation, a node receives a sample of
opinions from a limited number of neighbors chosen uniformly at random. Each
activated node then adopts the opinion that is least common within the received
sample. Unlike all other known consensus dynamics, we prove that this
elementary protocol behaves in dramatically different ways, depending on
whether activations occur sequentially or in parallel. Specifically, we show
that its expected consensus time is exponential in $n$ under asynchronous
models, such as asynchronous GOSSIP. On the other hand, despite its chaotic
nature, we show that it converges within $O(\log^2 n)$ rounds with high
probability under synchronous models, such as synchronous GOSSIP. Finally, our
results shed light on the bit-dissemination problem, that was previously
introduced to model the spread of information in biological scenarios.
Specifically, our analysis implies that the minority-opinion dynamics is the
first stateless solution to this problem, in the parallel passive-communication
setting, achieving convergence within a polylogarithmic number of rounds. This,
together with a known lower bound for sequential stateless dynamics, implies a
parallel-vs-sequential gap for this problem that is nearly quadratic in the
number $n$ of nodes. This is in contrast to all known results for problems in
this area, which exhibit a linear gap between the parallel and the sequential
setting.
