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Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

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  • Yu-Hsien Liao

    (Department of Applied Mathematics, National Pingtung University, Pingtung County 900391, Taiwan)

Abstract

In many interactive environments, operators may have to deal with different work objectives at the same time. In a realistic context, such as differences in the target type to be addressed, or changes in the behavior of other operators, operators may therefore have to cope with by adopting different work levels (strategies) at any given time. On the other hand, the importance or influence brought by operators may vary depending on many subjective and objective factors, such as the size of the constituency represented by a congressman, and the bargaining power of a business personnel which may vary. Therefore, it is reasonable that weights are apportioned to operators and arbitrary usability should be distributed according to these weights under various working levels and multiattribute situations. In pre-existing results for allocation rules, weights might be always apportioned to the “operators” or the “levels” to modify the differences among the operators or its working levels respectively. By applying weights to the operators and its working levels (strategies) simultaneously, we adopt the maximal marginal variations among working level (strategy) vectors to propose an allocation rule under multiattribute situations. Furthermore, we introduce some axiomatic outcomes to display the rationality for this weighted allocation rule. By replacing weights to be maximal marginal variations, a generalized index is also introduced.

Suggested Citation

  • Yu-Hsien Liao, 2021. "Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:617-:d:517128
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