9
spatial modeling work with probabilistic voting and variable voter turnout (Enelow and
Hinich, 1989). However matters are quite different when voters exhibit partisan loyalties
(i.e. b>0). In this situation it is easily verified from equations 1-2 that 0
< c
D
< 1 and 0
< c
R
< 1,
6
and hence that as a
→
0 each candidates’ equilibrium position diverges to a location
between the mean voter position and the mean position of the candidate’s partisan con-
stituency. We therefore conclude that when voters display partisan biases and abstention is
from alienation, each candidate’s margin-maximizing position is shifted away from the
center, in the direction of the mean position of the candidate’s partisan constituency.
More specifically, equations 1-2 imply that when voters display partisan biases and
a
→
0, the following relationships hold: First, ceterus paribus, the more extreme the position
of the candidate’s partisan constituency, the further the candidate diverges from the cen-
ter, in the direction of this constituency.
7
Second, again ceterus paribus, the larger the
candidate’s partisan constituency the further the candidate diverges from the center, in the
direction of this constituency.
8
Why, specifically, are margin-maximizing candidates motivated to shift away from
the center in the direction of their partisans? The reason is that the marginal change in a
candidate’s probabilities of attracting her own partisans’ votes via policy appeals is higher
than is the marginal change in her probabilities of attracting votes from the rival candi-
date’s partisans. To understand why this is true, note that the properties of the conditional
logit (CL) probability function imply that the weight w
i
that a candidate attaches to a voter
i’s policy preference increases as the probability that i votes for the candidate approaches
0.5 (from either direction).
9
This conforms to common sense: the more uncommitted the
voter’s decision to turn out to vote for a candidate, the more the candidate will take the
6
To see this, note that in equations 1 and 2, the denominators are equal to the numerator plus a positive term.
7
This follows from the fact that the functions c
1
and c
2
are, by inspection, invariably positive.
8
To see this, note that the numerator and the first term in the denominator of equation 1-2 are each identical
positive functions of
D
m
or
R
m
, while the denominator contains a second positive term.
9
This is also true for the multinomial probit probability function, in the general case where the correlations
between the error terms associated with the candidates’ utilities are set to zero, and the error terms have equal
variances.
Convention