Monotonic Norms and Orthogonal Issues in Multidimensional Voting

Alex Gershkov (), Benny Moldovanu () and Xianwen Shi

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We study issue-by-issue voting by majority and incentive compatibility in multi- dimensional frameworks where privately informed agents have preferences induced by general norms and where dimensions are endogenously chosen. We uncover the deep connections between dominant strategy incentive compatibility (DIC) on the one hand, and several geometric/functional analytic concepts on the other. Our main results are: 1) Marginal medians are DIC if and only if they are calculated with respect to coor- dinates de ned by a basis such that the norm is orthant-monotonic in the associated coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are computed with respect to a basis such that, for any vector in the basis, any linear combination of the other vectors is Birkho¤-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to nd all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for lp spaces of any nite dimension, and show that they do not depend on p (unless p = 2).

JEL-codes: D71 D82 (search for similar items in EconPapers)
Pages: 36
Date: 2021-04
New Economics Papers: this item is included in nep-des and nep-ore
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.crctr224.de/research/discussion-papers/archive/dp290 (application/pdf)

Related works:
Journal Article: Monotonic norms and orthogonal issues in multidimensional voting (2020)
Working Paper: Monotonic Norms and Orthogonal Issues in Multidimensional Voting (2019)
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:bon:boncrc:crctr224_2021_290

Access Statistics for this paper

More papers in CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany Kaiserstr. 1, 53113 Bonn , Germany.
Bibliographic data for series maintained by CRC Office ().