A Unified Theory of Voting: Directional and Proximity by Samuel Merrill III, Bernard Grofman

By Samuel Merrill III, Bernard Grofman

Professors Merrill and Grofman boost a unified version that comes with voter motivations and assesses its empirical predictions--for either voter selection and candidate strategy--in the us, Norway, and France. The analyses convey blend of proximity, course, discounting, and occasion identification fit with the mildly yet no longer tremendous divergent regulations 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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Vn cn is the scalar or dot product of i =1 the vectors V and C representing voter and candidate, respectively, and q is the angle between V and C. 8 In a one-dimensional model, there are only two directions (right and left). With the exception of degenerate cases, the Matthews utility is either +1 or -1 according to whether the voter agrees or does not agree with the candidate on the single issue. In a twocandidate race, the candidate with a majority on her side of the neutral point wins; if both are on the same side, they tie.

1). 0 degrees. Voters between these two lines have opposite preferences under the two models, reflecting the voters’ reactions to the first candidate’s intensity. 4 degrees, approximately halfway between the indifference lines for the pure models. Accordingly, as a rough approximation, we can interpret the vector C, the RM utility function can be expressed as a product of the Matthews utility function and a pure intensity component as follows: Ê V◊C U ( V, C) = V ◊ C = Á Ë V C 5 ˆ ˜( V C ) ¯ In a one-dimensional model, V and B are scalars.

In Chapter 10, we give a necessary and sufficient condition that a candidate not vote for herself under the RM model. 32 Part I Models of Voter Behavior If, under the RM model, there are only two candidates – but with one on the left and one on the right – each takes the entire vote on his side of the neutral point and movement toward the extreme or toward the center (without crisscrossing) makes no difference in vote share. In this case there is no incentive to move toward the center. Indeed, in a race with three or more candidates, the interior candidates would have strong incentives to leapfrog more extreme opponents.

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