Minimally strategy-proof rank aggregation

Hayrullah Dindar, Onur Doğan and Jean Lainé
Additional contact information
Onur Doğan: Murat Sertel Center - Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University

Post-Print from HAL

Abstract: A rank aggregation rule aggregates finitely many linear orderings of objects to a collective linear ordering of these objects. We consider the robustness of rank aggregation methods to manipulation by misrepresentation of some individual order. This requires formulating assumptions about how individuals compare orders. Betweenness is a natural assumption for rank aggregation rules interpreted as Arrowian aggregation rules, which maps every family of individual preferences over social alternatives to a collective preference over those alternatives. However, many rank aggregation rules do not relate to the classical preference aggregation problem, and call for different assumptions. Instead of focusing on specific assumptions, we only assume that individuals compare orders by means of an order extension, which maps every linear order p over objects to a linear order over orders which places p at top. We define as minimally strategy-proof a rank aggregation rule that cannot be manipulated with respect to at least one order extension. We characterize the class of minimal strategy-proof rules. Based on this characterization, we show that most rules considered in Bossert and Sprumont (2014) and Athanasoglou (2016, 2019) are not minimally strategy-proof (while being betweenness strategy-proof). This emphasizes the critical role of linearity when imposed to order extensions. Moreover, we show that a rule is strategy-proof for a rich domain of order extensions if and only if it is either constant or dictatorial, where richness requires that each ordering of a pair of orders can prevail in some hyper-order. We also discuss the existence of rules that are strategy-proof for all order extensions that satisfy the Kemeny distance criterion.

Keywords: Rank; aggregation; -; Strategy-proofness; -; Order; extension; -; Betweenness; -; Kemeny; distance (search for similar items in EconPapers)
Date: 2024-11-22
References: Add references at CitEc
Citations:

Published in Social Choice and Welfare, 2024, ⟨10.1007/s00355-024-01569-4⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04841569

DOI: 10.1007/s00355-024-01569-4

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().