  Strongly opinionated minorities can have a dramatic impact on the opinion
dynamics of a large population. Two factions of inflexible minorities,
polarised into two competing opinions, could lead the entire population to
persistent indecision. Equivalently, populations can remain undecided when
individuals sporadically change their opinion based on individual information
rather than social information. Our analysis compares the cross-inhibition
model with the voter model for decisions between equally good alternatives, and
with the weighted voter model for decisions among alternatives characterised by
different qualities. Here we show that cross-inhibition, differently from the
other two models, is a simple mechanism, ubiquitous in collective biological
systems, that allows the population to reach a stable majority for one
alternative even in the presence of asocial behaviour. The results predicted by
the mean-field models are confirmed by experiments with swarms of 100 locally
interacting robots. This work suggests an answer to the longstanding question
of why inhibitory signals are widespread in natural systems of collective
decision making, and, at the same time, it proposes an efficient mechanism for
designing resilient swarms of minimalistic robots.
