94-06-042
Abstract:
The Dynamics of Adaptive Parties under Spatial Voting
John H. Miller and Peter F. Stadler
We explore the dynamics of a model of two-party competition under spatial
voting. the parties are allowed to {\it incrementally} adapt their platforms by
following the voting gradient imposed by the preferences of the electorate and
platform of the opposition. The emphasis in this model is on the dynamic system
formed by these conditions, in particular, we examine the characteristics of the
transient paths and the convergence points of the evolving platforms. We find that
in a simple spatial model with probabilistic voting, regardless of the initial
platsforms of each party, platforms eventually converge to a unique, globally
stable equilibrium matching the strength-weighted mean of the voters' preferred
positions. This result holds even if we allow simple cross-issue weightings,
however, if we allow nonlinear weighting functions many dynamic possibilities
occur, including multiple equilibria and, perhaps, limit cycles.
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