By Samuel Merrill III, Bernard Grofman
Professors Merrill and Grofman strengthen a unified version that comes with voter motivations and assesses its empirical predictions--for either voter selection and candidate strategy--in the U.S., Norway, and France. The analyses convey mix of proximity, path, discounting, and celebration identification fit with the mildly yet no longer tremendous divergent guidelines which are attribute of many two-party and multiparty electorates. All of those motivations are essential to comprehend the linkage among candidate factor positions and voter personal tastes.
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Additional info for A Unified Theory of Voting: Directional and Proximity Spatial Models
Issue is important to them (Rabinowitz and Macdonald, 1989). Likewise, candidates are assumed to vary in the intensity with which they advocate one or the other of two possible positions on each dichotomous issue. These assumptions are no different from those made in our interpretation of the Matthews, model, and – just as for the latter model – voter preference in the RM model depends on the interaction of voter and candidate intensities. For the RM model, however, utility not only reflects the relative salience of different issues to voters and candidates but also varies as the overall intensity of voter or candidate increases.
We have indicated that it is reasonable to combine directional, intensity, and proximity ideas in a single model because all may influence voter behavior. , challengers without a track record). It is important to recognize that mixing directional and proximity ideas is not mixing apples and oranges, since these pure models can be shown to be arrayable on a single continuum, and thus distinguishable by a single parameter. To draw together these perspectives, Merrill and Grofman (1997a) introduce a unified model specified by two parameters.
The unified model is defined by the utility function8 U (V, C) = 2(1 - b) V◊C V C q [ V C ] -b V-C 2 where b is a mixing parameter between directional and proximity components, and q is an intensity parameter. If q = 1, the unified model 8 Here, again, V · C denotes the scalar product of the vectors V and C. 1. Summary of pure models as special cases of the unified model and specification of utility functions Model b q d U(V, C) Pure proximity (Downs) 1 NA 1 - V - C = -Â (vi - ci ) Pure direction (Matthews) 0 0 NA Direction plus intensity (RM) 0 1 NA Proximity plus discounting (Grofman) 1 n 2 2 i =1 V◊C = cos q V C n Unified model Basic version: Discounting version: V ◊ C = Â vi ci i =1 NA 2 n d<1 - V - dC = - Â (vi - dci ) 2 i =1 a a NA 2( 1 - b ) V◊ C q [ V C ] -b V -C V C a a d<1 2( 1 - b ) V◊ C q [ V C ] - b V - dC V C 2 2 a Not restricted.
A Unified Theory of Voting: Directional and Proximity Spatial Models by Samuel Merrill III, Bernard Grofman