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Ranking by weighted sum

Author

Listed:
  • Tapan Mitra

    (Cornell University)

  • Kemal Ozbek

    (University of Southampton)

Abstract

When choosing an alternative that has multiple attributes, it is common to form a weighted sum ranking. In this paper, we provide an axiomatic analysis of the weighted sum criterion using a general choice framework. We show that a preference order has a weak weighted sum representation if it satisfies three basic axioms: Monotonicity, Translation Invariance, and Substitutability. Further, these three axioms yield a strong weighted sum representation when the preference order satisfies a mild condition, which we call Partial Representability. A novel form of non-representable preference order shows that partial representability cannot be dispensed in establishing our strong representation result. We consider several related conditions each of which imply a partial representation, and therefore a strong weighted sum representation when combined with the three axioms. Unlike many available characterizations of weighted sums, our results directly construct a unique vector of weights from the preference order, which makes them useful for economic applications.

Suggested Citation

  • Tapan Mitra & Kemal Ozbek, 2021. "Ranking by weighted sum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 511-532, September.
    • Handle: RePEc:spr:joecth:v:72:y:2021:i:2:d:10.1007_s00199-020-01305-w
    DOI: 10.1007/s00199-020-01305-w
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    References listed on IDEAS

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    Cited by:

    1. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "An axiomatic approach towards pandemic performance indicators," Economic Modelling, Elsevier, vol. 116(C).

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