Spatial Voting Models: A Dynamical Systems Approach

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Steverango, Luke
spatial voting models , dynamical systems , game theory
Spatial voting models have been used extensively to study factors affecting candidate positioning in elections. Most previous research has fixed candidate positioning at one point in time to determine optimal candidate payoff. In this paper we examined candidate positioning within a dynamical system, thereby adding a temporal component to the analysis that allowed for a more realistic model of candidate behaviour in the lead-up to an election. Using a two-candidate and one-voting bloc case, the results from this research identified several critical points that described different types of candidate equilibria. Competitive critical points mirrored findings in previous research. Flip-Flop and Noncompetitive points, however, identified sub-optimal candidate positions that might arise during an election. Flip-flop points appeared to highlight situations in which candidates oscillated between trying to outmaneuver their opponent and attempting to move closer to their ideological positions. Noncompetitive points seemed to describe candidate intransigence regarding their policies. Bifurcation analysis revealed how the dynamical system was affected by subtle differences in the voting bloc’s position. We also examined the relationship between the Nash equilibrium solution concept and asymptotic stability of critical points. Although our findings suggested that Nash equilibrium points are always asymptotically stable critical points, the converse was not necessarily true. Future studies might extend this spatial voting model by increasing the number of candidates or weighting the voting blocs to see how these changes affect the dynamics. Additional research could also investigate whether it is true that an asymptotically stable critical point with complex eigenvalues is never a Nash equilibrium point in all dynamical systems.
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