www-ai.cs.tu-dortmund.de/LEHRE/SEMINARE/SS21/TrustworthyAIMachineLearning/garcia2020a.pdf
satisfaction proba- bility, and so on.
Example 4. In Examples 1 and 2 we have F1 ↑ = F2 ↑ = (1, 2 3 ,
2 3 ,
2 3 ) ≻
D ↑ = ( 23 , 2 3 ,
2 3 ,
2 3 ). As D ↑ is not lexicographically maximal, it cannot be maxmin- [...] the fact that F ↑ [D1 ∪ D2] ↑ implies F2 ↑ D2 ↑, and the maxmin-fairness of D2 allows us to deduce that F2 ↑= D2 ↑. Hence, by Lemma 1, for all v /∈ B1 we have F [v] = F2[v] = D2[v].
Similarly, we have the [...] probabilities of a0, a1, a2 and a3 are then 1, 2 3 ,
2 3 ,
2 3 . Any attempt to
match, say, a1 with probability > 2 3 will necessarily result in satisfaction probabil-
ity < 2 3 for a2 or a3. Another maxmin-fair …
