Role of the plurality rule in multiple choices
  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. 
Angelo M. Calv\~ao and Marlon Ramos and Celia Anteneodo
physics.soc-ph cond-mat.stat-mech