Abstention causes bifurcations in two-party voting dynamics

In a recent dynamical systems model of platform adaptation in spatial voting models, Miller and Stadler (J.H. Miller, P.F. Stadler, J. Econ. Dyn. and Control 23 (1998) 171–189) showed that, assuming concave voter utility functions and complete participation, there is a globally stable equilibrium lo...

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Bibliographic Details
Published in:Applied mathematics and computation 2000-09, Vol.114 (2), p.215-232
Main Author: Stadler, Bärbel M.R.
Format: Article
Language:English
Subjects:
Abstention
Adaptive dynamics
Applied sciences
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Portfolio theory
Spatial voting models
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Summary:In a recent dynamical systems model of platform adaptation in spatial voting models, Miller and Stadler (J.H. Miller, P.F. Stadler, J. Econ. Dyn. and Control 23 (1998) 171–189) showed that, assuming concave voter utility functions and complete participation, there is a globally stable equilibrium located at the mean voter position. Here we show that abstention depending on the distances between voters and platforms may lead to bifurcations rendering the mean voter equilibrium unstable. We find up to seven equilibria, up to four of which are local attractors for the platform dynamics.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(99)00114-9