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

By Samuel Merrill III, Bernard Grofman

Professors Merrill and Grofman enhance a unified version that includes voter motivations and assesses its empirical predictions--for either voter selection and candidate strategy--in the U.S., Norway, and France. The analyses express blend of proximity, path, discounting, and celebration identity have compatibility 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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Cn) denote the vectors of voter and candidate locations in n-dimensional issue space, vi and ci are the voter and candidate locations on the ith issue dimension, i = 1, . . 1 Note that a negative sign is used in defining this utility function, so that utility declines with distance. , X = n Âx i =1 2 i . Thus, ||V - C|| is the Euclidean distance between V and C; ||V - C||2 is squared Euclidean distance. , U(V, C) = -||V - C||. 2 for a comparison of these metrics. 2 The Grofman Discounting Model Grofman (1985) proposed two modifications of the standard proximity model: (1) accounting for the location of a status quo point and (2) explicit discounting of candidate positions.

Where would you place yourself on this scale, or haven’t you thought much about this? A voter’s reported position on this issue may be either an attempt for the voter to locate himself on a policy axis of governmental intervention or a reflection of the salience of the issue, or both. Thus a centrist placement may reflect preference for moderate government intervention, lack of interest in the issue, or some combination of these attitudes (Poole and Rosenthal, 1984a). An extreme position represents preference for a policy at one end of the policy spectrum, but may also represent strong interest in the issue.

But the proximity model assigns widely varying utilities to these latter two situations, reflecting the greater lengths of the vectors in plot c. In general, if both voter and candidate vectors (relative to a neutral point) are dilated by some factor, proximity utility is multiplied by that factor squared; in other words, proximity utility is quite sensitive to acrossthe-board changes in scale. The RM utility is also affected the same way, as can be seen by changing the lengths of either the voter or candidate vectors in plot b or e.

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