2023/02/15 by Christoph Börgers, Börgers, Christoph, Bruce M. Boghosian +5 · 1 citation
Decision Sciences · Physics and Astronomy · #37N40 #91F10 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Game Theory and Applications #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.2302.07993
openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move towards the other. This eventually results in two centrists with coalescing views. However, the strategy of moving towards the other candidate ceases to be optimal when enough voters abstain instead of voting for a centrist who does not represent their views. These observations, formalized in various ways, have been made many times. Our own formalization is based on differential equations. The surprise and main result derived from these equations is that the final candidate positions can jump discontinuously as the voters' loyalty towards their candidate wanes. The underlying mathematical mechanism is a blue sky bifurcation.