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On Ordered Weighted Averaging Social Optima

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Abstract

In this paper, we look at the classical problem of aggregating individual utilities and study social orderings which are based on the concept of Ordered Weighted Averaging Aggregation Operator. In these social orderings, called Ordered Weighted Averaging Social Welfare Functions, weights are assigned a priori to the positions in the social ranking and, for every possible alternative, the total welfare is calculated as a weighted sum in which the weight corresponding to the kth position multiplies the utility in the kth position. In the α-Ordered Weighted Averaging Social Welfare Function, the utility in the kth position is the kth smallest value assumed by the utility functions, whereas in the β-Ordered Weighted Averaging Social Welfare Function it is the utility of the kth poorest individual. We emphasize the differences between the two concepts, analyze the continuity issue, and provide results on the existence of maximum points.

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Notes

  1. That is, real valued functions defined over a fixed set of alternatives representing social states.

  2. The order is from the worst to the best.

  3. The dimension of this vector can be smaller than n and it depends on the alternative.

  4. To our knowledge, there are no results on this issue in the literature yet.

  5. A complete survey of the literature cannot be the purpose of this note.

  6. All the results contained in this paper could be easily extended to the infinite dimensional case under suitable assumptions.

  7. This is the classical generalized Weierstrass theorem.

  8. Things change in the infinite dimensional case in which only the sequential upper semicontinuity property would be required.

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Acknowledgements

The authors would like to thank the associate editor and two anonymous referees for helpful comments and suggestions. Giuseppe De Marco acknowledges the financial support provided by MIUR-PRIN 2010 Research Program “Robust decision making in markets and organizations”.

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Authors and Affiliations

  1. Department of Management and Quantitative Studies, University of Naples Parthenope, via Generale Parisi 13, Napoli, 80132, Italy

    Giuseppe De Marco

  2. CSEF, University of Naples Federico II, Via Cinthia, Napoli, 80126, Italy

    Giuseppe De Marco & Jacqueline Morgan

  3. Department of Economics and Statistics, University of Naples Federico II, Via Cinthia, Napoli, 80126, Italy

    Jacqueline Morgan

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  1. Giuseppe De Marco
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  2. Jacqueline Morgan
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Correspondence to Jacqueline Morgan.

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De Marco, G., Morgan, J. On Ordered Weighted Averaging Social Optima. J Optim Theory Appl 160, 623–635 (2014). https://doi.org/10.1007/s10957-013-0376-7

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  • DOI: https://doi.org/10.1007/s10957-013-0376-7

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