EDITOR’S PROOF
324 N. Schofield and B. Demirkaya
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The eigenvalues of the characteristic matrix are− 0 .06 with the eigenvector
(− 0. 961 ,− 0. 278 )and− 0 .403 with the eigenvector(− 0. 278 , 0. 961 ). We calcu-
late a confidence interval for the Hessian using the upper bound of theβcoefficient
and the lower bound ofρDTPand vice versa.
CDTP= 2 β( 1 − 2 ρDTP)∇−I
= 2 × 0. 538 ×( 1 − 2 × 0. 05 )∇−I, 2 × 0. 778 ×( 1 − 2 × 0. 01 )∇−I
= 0. 968
[
0 .729 0. 073
0 .073 0. 498
]
−I, 1. 525
[
0 .729 0. 073
0 .073 0. 498
]
−I
=
[
− 0. 294 0. 071
0. 071 − 0. 518
]
,
[
0. 112 0. 111
0. 111 − 0. 241
]
Theeigenvalues of the lower bound for the characteristic matrix are− 0 .273 with
the eigenvector(− 0. 96 ,− 0. 279 )and− 0 .539 with the eigenvector(− 0. 279 , 0. 96 ).
The eigenvalues of the upper bound for the characteristic matrix are 0.144 with the
eigenvector(− 0. 961 ,− 0. 277 )and− 0 .273 with the eigenvector(− 0. 277 , 0. 961 ).
As mentioned above, Schofield ( 2007 ) shows that a necessary and sufficient con-
dition for the electoral mean to be LNE is that the eigenvalues of the characteristic
matrix are both negative. As we see above, the point estimate and the lower bound
for the characteristic matrix have negative eigenvalues, which implies that the elec-
toral mean should be LNE. The upper bound for the characteristic matrix has one
positive and one negative eigenvalue, and a negative determinant(− 0. 15 ). Hence,
the upper bound gives a saddle point.
By simulation based on the point estimates of the spatial coefficients and the
valence terms, we can verify that the electoral mean is an LNE in our case. When
all the parties are located at the electoral mean their predicted vote shares were
calculated as:
ρz^0 =
(
ρzAKP^0 ,ρzCHP^0 ,ρMHPz^0 ,ρDTPz^0 ,ρDYPz^0 ,ρANAPz^0
)
=( 0. 543 , 0. 246 , 0. 132 , 0. 024 , 0. 03 , 0. 025 )
We compare this to votes shares in our sample:
(sAKP,sCHP,sMHP,sDTP,sDYP,sANAP)
=( 0. 556 , 0. 231 , 0. 134 , 0. 025 , 0. 03 , 0. 023 )
This comparison is important as it tells us about whether the low valence parties
have any incentive to move to the electoral mean. Schofield and Gallego ( 2011 , 190)
call an equilibrium at positionzastable attractorwhen the lower 95 % bound of
predicted vote shares of low valence parties at the equilibrium are higher than their
actual vote shares. If an equilibrium is not a stable attractor than the party activists
would have more incentive to pull the party from the electoral mean toz∗.Aswe
see in the vectors, the equilibrium at the electoral mean is not a stable attractor for
DTP or DYP.
