The independent variables were constructed exactly as in the previous chapter. In
addition to the data concerning the first dimension, TC also used a second dimension from Laver
and Hunt (1992). Laver and Hunt scored parties on the basis of their “pro friendly relations to
USSR vs. anti.” Note that this dimension is different from the left-right dimension. In fact, the
pair-wise correlation between the ideological distances based on these two dimensions in the
dataset only slightly above 0.5. However, parties scoring high in this second dimension are
parties of the left.
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The two-dimensional “ideological distance” and “alternation” variables. On the basis of
Proposition 1.4 we needed to know whether the unanimity core of one government is included in
the unanimity core of another. In a single dimension this is an easy task: one compares the length
of the core of two coalitions (the “range” as we did in Chapter 7). In two or more dimensions,
however, such a straightforward measure does not exist. For example, it is not true that if the
unanimity core of coalition A covers a larger area than the unanimity core of coalition B then A
necessarily includes B (that is the relevant criterion according to Figure 1). For example, if a
coalition has two distant members, (which by definition means that its unanimity core is a
straight line and therefore covers an area of zero) it can make decisions more easily than a
coalition with three members located close to each other (which covers a small but positive area).
As a result, TC approximate the ideological distances of different coalitions in two dimensions
by using the range of these coalitions in each dimension, and calculating their average. For
alternation, the selection of the indicator was easier because we knew the position of the middle
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Some examples from our dataset: in 1988 when the Schluter cabinet in Denmark experienced a government
reformation from a coalition of the Conservatives, the Liberal and the central Democrats to a coalition of the
Conservatives, the Liberal and the Radical Liberals, we find that the ideological range in the second index changes
from 1.6 to 5, while the ideological range in the first index only changes from 5.6 to 4.9. Similarly, in Australia,
1983, when the Fraser cabinet (which consists of the National party and the Liberal party) was replaced by the
Hawke cabinet (the Labor party), the ideological position of government in the second index shifted from 12.59 to
7.29, while the ideological position in the first index only changed from 14.86 to 10.10.