Miller, J. H.,Stadler, P. F.

We explore the dynamics of a model of two-party competition under spatial voting. The parties are allowed to incrementally adapt their platforms by following the voting gradient imposed by the preferences of the electorate and the 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 platforms of each party, platforms eventually converge to a unique, globally stable equilibrium matching the strength-weighted mean of the voters' preferred positions. This result appears robust to many variations in voter preferences and party behavior. However, we do find some conditions under which other dynamic possibilities occur, including multiple equilibria and, perhaps, limit cycles. (C) 1998 Elsevier Science B.V. All rights reserved.