IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.07773.html
   My bibliography  Save this paper

Axiomatic characterization of pointwise Shapley decompositions

Author

Listed:
  • Marcus C Christiansen

Abstract

A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the decomposition of functions with real arguments, a popular method is the pointwise application of the Shapley value on the domain. However, this pointwise application largely ignores the overall structure of functions. In this paper, axioms are developed which fully preserve functional structures and lead to unique decompositions for all Borel measurable functions.

Suggested Citation

  • Marcus C Christiansen, 2023. "Axiomatic characterization of pointwise Shapley decompositions," Papers 2303.07773, arXiv.org.
    • Handle: RePEc:arx:papers:2303.07773
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.07773
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Sequential decompositions at their limit," Papers 2212.06733, arXiv.org, revised Apr 2023.
    2. Nicholas Moehle & Stephen Boyd & Andrew Ang, 2021. "Portfolio Performance Attribution via Shapley Value," Papers 2102.05799, arXiv.org.
    3. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Sequential decompositions at their limit," Papers 2212.06733, arXiv.org, revised Apr 2023.
    2. Bruch, Sarah K. & van der Naald, Joseph & Gornick, Janet C., 2022. "Poverty Reduction through Federal and State Policy Mechanisms: Variation Over Time and Across the U.S. States," SocArXiv jz5xp, Center for Open Science.
    3. Nicolas Hérault & Guyonne Kalb, 2022. "Understanding the rising trend in female labour force participation," Fiscal Studies, John Wiley & Sons, vol. 43(4), pages 341-363, December.
    4. Pedro Salas-Rojo & Juan Gabriel Rodríguez, 2022. "Inheritances and wealth inequality: a machine learning approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 27-51, March.
    5. Tiwari,Sailesh & Lara Ibarra,Gabriel & Narayan,Ambar, 2015. "How unfair is the inequality of wage earnings in Russia ? estimates from panel data," Policy Research Working Paper Series 7291, The World Bank.
    6. Antonio Abatemarco & Massimo Aria & Sergio Beraldo & Michela Collaro, 2023. "Measuring Access and Inequality of Access to Health Care: a Policy-Oriented Decomposition," CSEF Working Papers 666, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    7. David Pérez-Mesa & à ngel S. Marrero, 2024. "Adult health and inequality of opportunity in Spain," Working Papers 671, ECINEQ, Society for the Study of Economic Inequality.
    8. Zengzeng Fan & Wei Zou, 2023. "A Three-Component Decomposition of the Change in Relative Poverty: An Application to China," Land, MDPI, vol. 12(1), pages 1-15, January.
    9. Gaurav Datt, 2019. "Multidimensional poverty in the Philippines, 2004–2013: How much do choices for weighting, identification and aggregation matter?," Empirical Economics, Springer, vol. 57(4), pages 1103-1128, October.
    10. Gregorio Gimenez & Ana Isabel Gil-Lacruz & Marta Gil-Lacruz, 2021. "Is Happiness Linked to Subjective Life Expectancy? A Study of Chilean Senior Citizens," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    11. Brunori, Paolo & Ferreira, Francisco & Lugo, Maria Ana & Peragine, Vito, 2013. "Opportunity-sensitive poverty measurement," Policy Research Working Paper Series 6728, The World Bank.
    12. Touhami Abdelkhalek & Dorothee Boccanfuso, 2023. "Is the Moroccan Fiscal System Progressive ? A Shapley Decomposition," Policy briefs on Economic Trends and Policies 2342, Policy Center for the New South.
    13. Marko Ledić & Ivica Rubil, 2021. "Beyond Wage Gap, Towards Job Quality Gap: The Role of Inter-Group Differences in Wages, Non-Wage Job Dimensions, and Preferences," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 155(2), pages 523-561, June.
    14. Pera, Rebecca & Viglia, Giampaolo & Furlan, Roberto, 2016. "Who Am I? How Compelling Self-storytelling Builds Digital Personal Reputation," Journal of Interactive Marketing, Elsevier, vol. 35(C), pages 44-55.
    15. Daniela Piazzalunga & Maria Laura Di Tommaso, 2019. "The increase of the gender wage gap in Italy during the 2008-2012 economic crisis," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(2), pages 171-193, June.
    16. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1085-1140.
    17. Buckle, Robert A. & Creedy, John & Ball, Ashley, 2020. "A Schumpeterian Gale: Using Longitudinal Data to Evaluate Responses to Performance-Based Research Funding Systems," Working Paper Series 9447, Victoria University of Wellington, Chair in Public Finance.
    18. Jacques Silber & Sasiwimon Warunsiri Paweenawat & Lusi Liao, 2022. "On the measurement of non-random mating and of its change over time," Review of Economics of the Household, Springer, vol. 20(1), pages 161-198, March.
    19. Dean F. Amel & Robin A. Prager, 2016. "Community Bank Performance: How Important are Managers?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 48(2), pages 149-180, March.
    20. Pérez-Mesa, David & Marrero, Gustavo A. & Darias-Curvo, Sara, 2021. "Child health inequality in Sub-Saharan Africa," MPRA Paper 108801, University Library of Munich, Germany.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2303.07773. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.