Ranking by weighted sum

Tapan Mitra and Kemal Ozbek ()
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Kemal Ozbek: University of Southampton

Economic Theory, 2021, vol. 72, issue 2, No 5, 532 pages

Abstract: 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.

Keywords: Decomposition of the set of irrationals; Partial representation; Substitutability; Weak representation; Weighted sum; D01; D60; D70 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00199-020-01305-w

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