On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions

Souvik Roy and Soumyarup Sadhukhan

MPRA Paper from University Library of Munich, Germany

Abstract: We consider a weaker notion of strategy-proofness called upper contour strategy-proofness (UCSP) and investigate its relation with strategy-proofness (SP) for random social choice functions (RSCFs). Apart from providing a simpler way to check whether a given RSCF is SP or not, UCSP is useful in modeling the incentive structures for certain behavioral agents. We show that SP is equivalent to UCSP and elementary monotonicity on any domain satisfying the upper contour no restoration (UCNR) property. To analyze UCSP on multi-dimensional domains, we consider some block structure over the preferences. We show that SP is equivalent to UCSP and block monotonicity on domains satisfying the block restricted upper contour preservation property. Next, we analyze the relation between SP and UCSP under unanimity and show that SP becomes equivalent to UCSP and multi-swap monotonicity on any domain satisfying the multi-swap UCNR property. Finally, we show that if there are two agents, then under unanimity, UCSP alone becomes equivalent to SP on any domain satisfying the swap UCNR property. We provide applications of our results on the unrestricted, single-peaked, single-crossing, single-dipped, hybrid, and multi-dimensional domains such as lexicographically separable domains with one component ordering and domains under committee formation.

Keywords: strategy-proofness; upper contour strategy-proofness; unanimity; elementary monotonicity; block monotonicity; multi-swap monotonicity (search for similar items in EconPapers)
JEL-codes: D71 D81 (search for similar items in EconPapers)
Date: 2020-08-21
New Economics Papers: this item is included in nep-des
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/104405/1/MPRA_paper_104405.pdf original version (application/pdf)

Related works:
Journal Article: On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions (2022)
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:pra:mprapa:104405

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().