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Fair division under interval uncertainty. (English) Zbl 1113.68542

Summary: It is often necessary to divide a certain amount of money between \(n\) participants, i.e., to assign, to each participant, a certain portion \(w_{i}\geq 0\) of the whole sum (so that \(w_{1}+ \dots + w_{n}=1)\). In some situations, from the fairness requirements, we can uniquely determine these “weights” \(w_{i}\). However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals \([w_i^-,w_i^+]\) of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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[1] DOI: 10.1007/978-1-4613-3440-8_11
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