  People are often challenged to select one among several alternatives. This
situation is present not only in decisions about complex issues, e.g.,
political or academic choices, but also about trivial ones, as in daily
purchases at a supermarket. We tackle this scenario by means of the tools of
statistical mechanics. Following this approach, we introduce and analyze a
model of opinion dynamics, using a Potts-like state variable to represent the
multiple choices, including the ``undecided state'', that represents the
individuals that do not make a choice. We investigate the dynamics over
Erd\"{o}s-R\'enyi and Barab\'asi-Albert networks, two paradigmatic classes with
the small-world property, and we show the impact of the type of network on the
opinion dynamics. Depending on the number of available options $q$ and on the
degree distribution of the network of contacts, different final steady states
are accessible: from a wide distribution of choices to a state where a given
option largely dominates. The abrupt transition between them is consistent with
the sudden viral dominance of a given option over many similar ones. Moreover,
the probability distributions produced by the model are validated by real data.
Finally, we show that the model also contemplates the real situation of
overchoice, where a large number of similar alternatives makes the choice
process harder and indecision prevail.
