VOTING-BEHAVIOR UNDER THE DIRECTIONAL SPATIAL MODEL OF ELECTORAL COMPETITION

This paper contrasts voting behavior in multicandidate elections betwe en the proximity and the directional spatial models of electoral compe tition. Under the traditional proximity spatial model, a voter's utili ty for a candidate is a declining function of distance between their r espective Positions. Under the directional spatial model, introduced b y Rabinowitz and Macdonald, utility is specified as the scalar product of the vectors representing voter and candidate. The present paper sp ecifies and compares regions of candidate support for the two models a nd for several voting procedures. The degree to which each model and v oting system favors extremist versus centrist candidates is assessed. It is shown that a pure directional model implies that candidates lyin g in the interior of the convex hull of the other candidates receive n o support under the single-vote plurality procedure. A one-parameter f amily of mixed proximity and directional models may provide more plaus ible descriptions of voter behavior than either pure model.