Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

Yu-Hsien Liao

doi:10.3390/math9060617

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.

Highlights

The mapping ht could be pondered as a power evaluation which appoints to every tactic vector α =s∈O ∈ FO the power that the agents could dedicate if every agent s takes operational strategy αs ∈ Fs in an acts affairs committee
Differing from existing investigations, we introduced the weighted lower-aggregate multiattribute index (WLAMI), weighted regular multiattribute index (WRMI), weighted upper-aggregate multiattribute index (WUAMI), and related axiomatic outcomes by applying weights to the operators and its working levels simultaneously under multiattribute multi-choice situations
We considered that all operators possess different working levels of participation; In a multitude of multi-choice game literature on allocation rules, it might be assumed that all operators possess different working levels of participation, most literature determined the value of a specific operator presented with a specific working level of participation, such as Hwang and

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Based on notion the equal allocation of non-separable costs (EANSC, Ransmeier [11]), Liao et al [12] introduce two allocation rules by assigning weights to the operators and its activity levels (decisions) respectively under multiattribute multi-choice situations. Whether different rule concepts might be considered by applying weights to the operators and its working levels (strategies) simultaneously under multiattribute multi-choice situations. Maximal marginal variations instead of weights naturally, different allocation rules and related axiomatic outcomes are introduced under multiattribute multi-choice situations

Definitions and Notations

Motivating and Practical Examples

Different Weighted Extension

Other Generalizations and Revised Stability

Conclusions

Methods