Ranking by weighted sum
Ranking by weighted sum
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.
Decomposition of the Set of Irrationals, Partial Representation, Substitutability, Weak Representation, Weighted Sum
Mitra, Tapan
11b6191f-9af6-44dc-a437-a3b0cb72ed66
Ozbek, Kemal
e7edfcf5-cb17-4e64-bfa4-30fb527d2e46
Mitra, Tapan
11b6191f-9af6-44dc-a437-a3b0cb72ed66
Ozbek, Kemal
e7edfcf5-cb17-4e64-bfa4-30fb527d2e46
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.
Text
WUR_July31
- Accepted Manuscript
More information
Accepted/In Press date: 3 August 2020
e-pub ahead of print date: 9 August 2020
Additional Information:
Publisher Copyright:
© 2020, The Author(s).
Keywords:
Decomposition of the Set of Irrationals, Partial Representation, Substitutability, Weak Representation, Weighted Sum
Identifiers
Local EPrints ID: 443187
URI: http://eprints.soton.ac.uk/id/eprint/443187
ISSN: 0938-2259
PURE UUID: ceb6ea70-ada2-4edc-a45d-80a7c7b55a25
Catalogue record
Date deposited: 13 Aug 2020 16:38
Last modified: 12 Jul 2024 02:05
Export record
Altmetrics
Contributors
Author:
Tapan Mitra
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
