Valence Politics and Equilibrium in Spatial Election Models

Spatial models of two-party or two-candidatecompetition almost never have pure-strategy Nashequilibria when the issue space has more than onedimension. This paper shows that the introduction ofvalence issues can create conditions where equilibriaexist, even in a multidimensional setting. We derivesufficient conditions for the existence of equilibria,and characterize the spatial locations of twocompeting parties or candidates when such equilibriaexist. The party with the advantage on the valencedimension will generally take a moderate position onthe positional issues. We consider the implications ofthese results for public perceptions of the parties,incumbency advantages, and realigning elections.

[1]  D. Black.  The theory of committees and elections , 1959 .

[2]  Melvin J. Hinich,et al.  Ideology and the theory of political choice , 1994 .

[3]  G. Kramer.  Short-Term Fluctuations in U.S. Voting Behavior, 1896–1964 , 1971, American Political Science Review.

[4]  K. Shepsle.  Institutional Arrangements and Equilibrium in Multidimensional Voting Models , 1979 .

[5]  Kenneth S. Rogoff,et al.  Elections and Macroeconomic Policy Cycles , 1986 .

[6]  Melvin J. Hinich,et al.  Nonspatial Candidate Characteristics and Electoral Competition , 1982, The Journal of Politics.

[7]  Kenneth S. Rogoff,et al.  Equilibrium Political Budget Cycles , 1987 .

[8]  Morris P. Fiorina,et al.  Representatives, roll calls, and constituencies , 1974 .

[9]  Donald E. Stokes,et al.  Spatial Models of Party Competition , 1963, American Political Science Review.

[10]  David Butler,et al.  Political change in Britain , 1974 .

[11]  Alex Cukierman,et al.  Asymmetric information and the electoral momentum of public opinion polls , 1991 .

[12]  R. Arnold.  The logic of congressional action , 1990 .

[13]  Existence of electoral equilibria with probabilistic voting , 1988 .

[14]  Joseph E. Harrington,et al.  A Spatial Theory of Positive and Negative Campaigning , 1996 .

[15]  Charles R. Plott,et al.  A Notion of Equilibrium and Its Possibility Under Majority Rule , 1967 .

[16]  Asymmetric policy effects, campaign contributions, and the spatial theory of elections , 1992 .

[17]  H. Hotelling.  Stability in Competition , 1929 .

[18]  Gerald H. Kramer,et al.  On a Class of Equilibrium Conditions for Majority Rule , 1973 .

[19]  David R. Mayhew.  Congress: The Electoral Connection , 1975 .

[20]  David Austen-Smith,et al.  Interest groups, campaign contributions, and probabilistic voting , 1987 .

[21]  Scott L. Feld,et al.  Centripetal forces in spatial voting: On the size of the Yolk , 1988 .

[22]  M.Daniel Bernhardt,et al.  Candidate reputations and the 'incumbency effect' , 1985 .

[23]  R. McKelvey.  Intransitivities in multidimensional voting models and some implications for agenda control , 1976 .

[24]  James M. Enelow,et al.  A New Approach to Voter Uncertainty in the Downsian Spatial Model , 1981 .

[25]  Simon P. Anderson,et al.  Incumbency effects in political campaigns , 1992 .

[26]  William A. Barnett,et al.  Political Economy: Institutions, Competition and Representation , 1993 .

[27]  Peter C. Ordeshook,et al.  Models of strategic choice in politics , 1989 .

[28]  A. Downs.  An Economic Theory of Democracy , 1957 .

[29]  Daniel E. Ingberman.  Incumbent reputations and ideological campaign contributions in spatial competition , 1992 .

[30]  J. Ferejohn,et al.  Bargaining in Legislatures , 1989, American Political Science Review.

[31]  Richard D. McKelvey,et al.  Covering, Dominance, and Institution Free Properties of Social Choice , 1986 .

[32]  M. Laver.  Making and breaking governments , 1996 .

[33]  Gary W. Cox,et al.  The Uncovered Set and the Core , 1987 .