Split Societies, Elections, and Polls

In modern democracies, the outcomes of elections and referendums are often strikingly close to evenly split. To explain this phenomenon, we propose a simple model of binary voting inspired by the Ising model. Voters are represented as binary spins, with ferromagnetic coupling between neighbors and an additional weak antiferromagnetic coupling to aggregated opinion polls. The model exhibits a distinct split society phase, whose features resemble those observed in real-world elections: the electorate spontaneously divides into two spatially coherent domains with opposing views; overall support hovers around 50/50; and the interface between domains tends to align with geographic or historical boundaries - such as city edges, natural barriers, or former national borders - where neighbor coupling is weaker. We analyze the physical properties of this phase and identify the conditions under which it emerges. By comparing the model with empirical results from binary elections in various countries, we estimate the relevant parameters governing system behavior.

Finally, we examine an alternative coupling mechanism to opinion polls based on self-regulated voter engagement. In this variant, supporters of the leading candidate become less active and less likely to persuade others, while those backing the trailing candidate become increasingly mobilized - tending to equalize public support over time. This mechanism also introduces feedback from polling and can stabilize the system near a 50/50 equilibrium. From a physics perspective, it corresponds to a non-reversible Ising-like model with dynamically evolving couplings.

Full list of the authors:

• Piotr Szymczak, Stanisław Rakowski - University of Warsaw, Poland
• Olivier Devauchelle - Université Paris Cité, Paris, France
• Piotr Nowakowski - Ruder Boskovic Institut, Zagreb, Croatia

Coffee and tea will be available on the spot.