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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