[This paper considers the impact of certain types of policy related voting patterns on the existence and location of equilibrium strategies in the spatial model of two-candidate competition. In contrast to much of the previous literature, this paper makes a distinction between the aggregate level patterns of voting and the individual level variables which bring them about. By so doing the assumptions can focus on objects which have a more direct empirical referent, namely, the aggregate level support function and the distribution of ideal points. Using this approach, sufficient conditions are found for the existence of equilibrium which, although themselves strong, make considerably weaker demands on individuals than have been generally assumed in the literature. Thus, it is not necessary that each voter vote strictly with regard to policy but, rather, it is sufficient that in the electorate as a whole there is a moderate amount of policy related voting. Other results of the analysis are that policy related voting of any type seems to encourage candidates to converge towards the center, with support from extremists only accentuating this tendency. It is the candidate's most loyal supporters who seem to have the least influence over his policy position.]

The standard F test for linear restrictions in regression is relevant as a criterion but fails to capture the notion of tradeoff between bias and variance. Average squared distance criteria yield operational tests that are more appropriate, depending upon objectives. In the present paper two alternative criteria are developed. The first allows testing of the hypothesis that the average squared distance of a restricted estimator from the parameter point in k space is less than the average squared distance of the unrestricted, ordinary least squares estimator from the same parameter point. The second sets up a test of betterness of the restricted estimator over the unrestricted estimator of E(Y/X), where betterness is again defined in average squared distance.