Konwersatorium im. J.Pniewskiego i L.Infelda

In modern democracies, the outcomes of elections and referendums are oftenstrikingly close to evenly split. To explain this phenomenon, we propose asimple model of binary voting inspired by the Ising model. Voters arerepresented as binary spins, with ferromagnetic coupling between neighborsand an additional weak antiferromagnetic coupling to aggregated opinionpolls. The model exhibits a distinct split society phase, whose featuresresemble those observed in real-world elections: the electoratespontaneously divides into two spatially coherent domains with opposingviews; overall support hovers around 50/50; and the interface betweendomains tends to align with geographic or historical boundaries—such ascity edges, natural barriers, or former national borders—where neighborcoupling is weaker. We analyze the physical properties of this phase andidentify the conditions under which it emerges. By comparing the modelwith empirical results from binary elections in various countries, weestimate the relevant parameters governing system behavior.Finally, we examine an alternative coupling mechanism to opinion pollsbased on self-regulated voter engagement. In this variant, supporters ofthe leading candidate become less active and less likely to persuadeothers, while those backing the trailing candidate become increasinglymobilized—tending to equalize public support over time. This mechanismalso introduces feedback from polling and can stabilize the system near a50/50 equilibrium. From a physics perspective, it corresponds to anon-reversible Ising-like model with dynamically evolving couplings.