Dual Random Utility Maximisation

B Independence of the axioms - Theorem 2
B.1: Regularity, Weak Constant Expansion, Negative Expansion, but not Contraction
Consistency
See example in Table 2.
B.2: Regularity, Negative Expansion, Contraction Consistency, but not Weak Constant
Expansion
See example in Table 4.
B.3: Regularity, Weak Constant Expansion, Contraction Consistency, but not Negative
Expansion
{a, b, c} {a, b} {a, c} {b, c}
a
1
3
0
1
2
−
b
1
3
1
3
−
2
3
c
1
3
−
1
2
1
3
Table 6:
B.4: Negative Expansion, Contraction Consistency, Weak Constant Expansion, but
not Regularity
{a, b, c} {a, b} {a, c} {b, c}
a 1 0
1
2
−
b 0
1
3
−
2
3
c 0 −
1
2
1
3
Table 7:
C Independence of the axioms - Theorem 3
C.1: Modal Regularity (i), Modal Regularity (ii), but not Impact Consistency
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