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The mathematics of the ecological footprint revisited: An axiomatic approach

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  • Thomas Kuhn
  • Radomir Pestow

Abstract

In this paper, we take an axiomatic approach to the design of ecological footprint indices. Our focus is put on the heterogeneity of land with respect to types and regions, at the core of an inherent aggregation problem. We propose an axiomatic characterization of the ecological footprint index with two fundamentally new axioms, symmetry and independence, which can resolve the problem of land heterogeneity. It is shown that a unique index, up to an affine transformation, exists meeting the axiom system. This index simplifies the aggregation procedure considerably and avoids the need for a synthetic unit of measurement, like global hectares, as well as complex transformations of variables by means of weighting schemes. Our findings reveal differences with the Global Footprint Network (GFN) index, in particular with regard to the treatment of land heterogeneity. Finally, the axiomatic methodology employed may open up perspectives for the development of ecological measures in general, and especially of measures for sustainability and tipping points.

Suggested Citation

  • Thomas Kuhn & Radomir Pestow, 2024. "The mathematics of the ecological footprint revisited: An axiomatic approach," Journal of Industrial Ecology, Yale University, vol. 28(4), pages 727-735, August.
    • Handle: RePEc:bla:inecol:v:28:y:2024:i:4:p:727-735
    DOI: 10.1111/jiec.13520
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    References listed on IDEAS

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    1. Thomas Kuhn & Radomir Pestow & Anja Zenker, 2021. "An axiomatic characterization of a generalized ecological footprint," Journal of Environmental Economics and Policy, Taylor & Francis Journals, vol. 10(4), pages 391-399, October.
    2. Jason Venetoulis & John Talberth, 2008. "Refining the ecological footprint," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 10(4), pages 441-469, August.
    3. Niccolucci, V. & Bastianoni, S. & Tiezzi, E.B.P. & Wackernagel, M. & Marchettini, N., 2009. "How deep is the footprint? A 3D representation," Ecological Modelling, Elsevier, vol. 220(20), pages 2819-2823.
    4. Wackernagel, Mathis & Onisto, Larry & Bello, Patricia & Callejas Linares, Alejandro & Susana Lopez Falfan, Ina & Mendez Garcia, Jesus & Isabel Suarez Guerrero, Ana & Guadalupe Suarez Guerrero, Ma., 1999. "National natural capital accounting with the ecological footprint concept," Ecological Economics, Elsevier, vol. 29(3), pages 375-390, June.
    5. Enrico Casadio Tarabusi & Giulio Guarini, 2013. "An Unbalance Adjustment Method for Development Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 112(1), pages 19-45, May.
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