Year: 2026
Type: preprint
Abstract: Negative partisanship-where voter mobilization is driven primarily by aversion toward an opposing candidate rather than positive alignment-profoundly reshapes modern electoral dynamics. Here, we formulate a two-dimensional piecewise map to model campaign opinion dynamics, where voter abstention arises endogenously from a latent spectrum of voter activation barriers. We show that cross-candidate rejection sensitivity triggers a non-smooth collapse of abstention, dividing the phase space into an under-mobilized regime and a fully mobilized campaign regime. In symmetric elections with radicalized voter bases, spontaneous symmetry breaking via a pitchfork bifurcation gives rise to asymmetric polling attractors partitioned by mirror-symmetric basins of attraction, where early public perceptions-encoded in initial campaign conditions-act as a deterministic catalyst selecting candidate lead lock-in long before election day. For elevated cross-rejection, the symmetric equilibrium destabilizes via a period-doubling flip bifurcation, driving persistent anti-frontrunner polling swings. Rather than predicting static candidate hegemony, our model reveals that high negative partisanship turns elections into time-sensitive dynamical systems, where final election outcomes reflect discrete sampling snapshots of an oscillating campaign trajectory.
Source: arXiv (Cornell University)
Author: Fontanari, José F.
Institutions: Universidade de São Paulo, Instituto de Física de São Carlos
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223056983