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Table 4 The unordered aggregated preference and asymmetry matrices

From: The role of higher education in spatial mobility

\({\mathbf {V}}\) \(I_1\) \(I_2\) \(I_3\) \(I_4\)
(a) Preference matrix
\(I_1\) 0.0 1.0 2.0 3,0
\(I_2\) 2.0 0.0 2.0 3,0
\(I_3\) 1.0 1.0 0.0 3,0
\(I_4\) 0.0 0.0 0.0 0,0
\(\sum\) 3.0 2.0 4.0 9.0
N\(^\text {o}\) 2 1 3 4
Opposite preferences=2+1+1=4
\({\mathbf {A}}\) \(I_1\) \(I_2\) \(I_3\) \(I_4\)
(b) Asymmetry matrix
\(I_1\) 0,0 \(-\)1/3 1/3 1,0
\(I_2\) 1/3 0,0 1/3 1,0
\(I_3\) \(-\)1/3 \(-\)1/3 0,0 1.0
\(I_4\) \(-\)1.0 \(-\)1.0 \(-\)1.0 0.0
\(\sum\) \(-\)1.0 \(-\)5/3 1/3 3.0
N\(^\text {o}\) 2 1 3 4
Sum of the lower triangular=\(-\)10/3