In an election most people weigh up the pros and cons of the candidates before they choose who to vote for, but a few zealots may have strong, unchangeable views. In his simulations, Mobilia likens this situation to an array of randomly oriented magnetic spins, each of which can point “up” or “down”. An impurity with a spin that is fixed in one of these directions represents the zealot.

The amount of influence this impurity has on its neighbouring spins depends on how many interactions it has with them, and this is determined by the number of dimensions in the system. Mobilia calculated the effect of the impurity in one, two and three dimensions, where it would interact with two, four and six nearest neighbours, respectively.

He found that in a one-dimensional string of spins, the impurity swiftly aligned all of the spins with itself – the equivalent of a unanimous vote. In two dimensions, a ‘unanimous vote’ was also reached, but it took much longer for the spins to line up. In three dimensions, Mobilia found that the influence of the impurity is limited to a small region, which means that the zealot’s influence is greatly restricted.

“In real life, each voter interacts with more than two others, so it seems reasonable to expect that the two- and three-dimensional models would be more realistic than the one-dimensional version,” Mobilia told PhysicsWeb. “In three dimensions, not all of the voters are doomed to follow the zealot, and this seems more or less in agreement with our everyday experience.”

Mobilia is one of several researchers now refining the simple ‘voter model’ to include randomly scattered zealots, zealots with a range of opinions, and zealots with opposite views – for example, Democrat or Republican. Such sophisticated models could also improve our understanding of many physical systems, including the kinetics of certain chemical reactions, magnetic arrays and diffusion processes.