Advertisement

Fairness measures for decision-making and conflict resolution

  • Apoorva M. Sampat
  • Victor M. ZavalaEmail author
Research Article

Abstract

Allocating utility among stakeholders is a fundamental decision-making task that arises in complex organizations, social planning, infrastructures, and markets. In this work, we reconcile concepts of fairness from the perspectives of game theory, economics, statistics, and engineering by using an axiomatic approach. Our work reveals significant deficiencies in the social welfare allocation approach (which is widely used in the engineering literature) and highlights interesting and desirable properties and connections between Nash and entropy allocation approaches.

Keywords

Fairness Utility allocation Optimization Decision-making 

Notes

References

  1. Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math Finance 9(3):203–228MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bertsimas D, Farias VF, Trichakis N (2011) The price of fairness. Oper Res 59(1):17–31MathSciNetCrossRefzbMATHGoogle Scholar
  3. Cowell FA (2000) Measurement of inequality. In: Atkinson AB, Bourguignon F (eds) Handbook of income distribution, vol 1, pp 87–166Google Scholar
  4. Cowell FA, Kuga K (1981) Additivity and the entropy concept: an axiomatic approach to inequality measurement. J Econ Theory 25(1):131–143MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dowling AW, Ruiz-Mercado G, Zavala VM (2016) A framework for multi-stakeholder decision-making and conflict resolution. Comput Chem Eng 90:136–150CrossRefGoogle Scholar
  6. Hu J, Mehrotra S (2012) Robust and stochastically weighted multiobjective optimization models and reformulations. Oper Res 60(4):936–953MathSciNetCrossRefzbMATHGoogle Scholar
  7. Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43(3):513–518MathSciNetCrossRefzbMATHGoogle Scholar
  8. Kelly FP, Maulloo AK, Tan DK (1998) Rate control for communication networks: shadow prices, proportional fairness and stability. J Oper Res Soc 49(3):237–252CrossRefzbMATHGoogle Scholar
  9. Lan T, Kao D, Chiang M, Sabharwal A (2010) An axiomatic theory of fairness in network resource allocation. In: Proceedings of IEEE INFOCOMGoogle Scholar
  10. Moulin H (1991) Axioms of cooperative decision making. No. 15. Cambridge University Press, CambridgeGoogle Scholar
  11. Nash JF Jr (1950) The bargaining problem. Econom J Econom Soc 18:155–162MathSciNetzbMATHGoogle Scholar
  12. Pavlikov K, Uryasev S (2014) Cvar norm and applications in optimization. Optim Lett 8(7):1999–2020MathSciNetCrossRefzbMATHGoogle Scholar
  13. Pessino C, Fenochietto R (2010) Determining countries’ tax effort. Hacienda Pública Española/Revista de Economía Pública 195(4):65–87Google Scholar
  14. Raiffa H (1953) Arbitration schemes for generalized two-person games. Ann Math Stud 28:361–387MathSciNetzbMATHGoogle Scholar
  15. Rawls J (1971) A theory of justice. Harvard University Press, CambridgeGoogle Scholar
  16. Rockafellar RT, Uryasev S et al (2000) Optimization of conditional value-at-risk. J Risk 2:21–42CrossRefGoogle Scholar
  17. Roth AE (1979) An impossibility result concerningn-person bargaining games. Int J Game Theory 8(3):129–132CrossRefzbMATHGoogle Scholar
  18. Roth AE (2018) Axiomatic models of bargaining, Lecture notes in economics and mathematical systems #170, 1979. https://web.stanford.edu/~alroth/Axiomatic_Models_of_Bargaining.pdf. Accessed 3 Aug 2018
  19. Sampat AM, Hu Y, Sharara M, Aguirre-Villegas H, Ruiz-Mercado G, Larson RA, Zavala VM (2018) Coordinated markets for scalable management of organic waste and derived products [Under Review]Google Scholar
  20. Venkatasubramanian V (2017) How much inequality is fair? Mathematical principles of a moral, optimal, and stable capitalist society. Columbia University Press, New YorkCrossRefGoogle Scholar
  21. Venkatasubramanian V, Luo Y (2018) How much income inequality is fair? Nash bargaining solution and its connection to entropy. arXiv preprint arXiv:1806.05262
  22. Zavala VM, Kim K, Anitescu M, Birge J (2017) A stochastic electricity market clearing formulation with consistent pricing properties. Oper Res 65(3):557–576MathSciNetCrossRefzbMATHGoogle Scholar
  23. Zukerman M, Tan L, Wang H, Ouveysi I (2005) Efficiency-fairness tradeoff in telecommunications networks. IEEE Commun Lett 9(7):643–645CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical and Biological EngineeringUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations