A Blue Sky Bifurcation in the Dynamics of Political Candidates

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 toward the other. This eventually results in two centrists with coalescing views. However, the strategy of movi...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 131; no. 3; pp. 225 - 238
Main Authors Börgers, Christoph, Boghosian, Bruce, Dragovic, Natasa, Haensch, Anna
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis Ltd 15.03.2024
Subjects
Bifurcations
Differential equations
Elections
Mathematical analysis
Political behavior
Political campaigns
Voters
Voting
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Summary: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 toward the other. This eventually results in two centrists with coalescing views. However, the strategy of moving toward the other candidate is no longer 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 toward their candidate wanes. The underlying mathematical mechanism is a blue sky bifurcation.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2023.2286221