EURO 2024 Copenhagen
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1038. Defending the Weighted Geometric Mean Aggregation

Invited abstract in session TA-47: How to support complex decisions. Negotiating the trade-off between Social, Environmental and Economic values 3, stream Multiple Criteria Decision Analysis.

Tuesday, 8:30-10:00
Room: 50 (building: 324)

Authors (first author is the speaker)

1. Pavel Janda
2. Daniele Chiffi
Department of architecture and Urban Studies, Politecnico di Milano

Abstract

The weighted geometric mean (WGT) is a commonly discussed procedure for aggregating judgements in multicriteria decision analysis (MDA) and social epistemology, but it has drawbacks. We combine MDA and social epistemology results to defend the ratio judgements aggregation with the WGT. We argue that aggregation with the WGT overcomes many drawbacks if one aggregates ratio judgements instead of absolute judgements. We use an axiomatic approach to argue that one should aggregate ratio judgements (we especially favour odds) instead of absolute judgements for the following reasons. First, the mathematical structure underlying ratio judgements (and their aggregation with the WGT) allows one to satisfy many desirable axioms that – for absolute judgements – lead to undesirable results. For example, we avoid dictatorial decisions, can weigh experts' judgements according to their expertise, and satisfy unanimity. Secondly, aggregation of ratio judgements is better suited to control and mitigate possible manipulations such as rank reversal than aggregation of absolute judgements, which can improve legal and ethical aspects of decisions. We present an intuitive sufficient condition that, if met, avoids any rank reversal by adding or deleting alternatives. We also present a sufficient condition for preventing rank reversal for marginalisation, roughly speaking, when initially separated alternatives are transformed into a single alternative using disjunction.

Keywords

Status: accepted

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