Monotonic Norms and Orthogonal Issues in Multidimensional Voting

Alex Gershkov, Benny Moldovanu () and Xianwen Shi

Working Papers from University of Toronto, Department of Economics

Abstract: We study issue-by-issue voting and robust mechanism design in multidimensional frameworks where privately informed agents have preferences induced by general norms. 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 coordinates defined 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 Birkhoff-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to find all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for l_{p} spaces of any finite dimension, and show that they do not depend on p (unless p=2).

Keywords: Multidimensional Voting; Dominant Strategy; Monotonic Norms; Orthogonality (search for similar items in EconPapers)
JEL-codes: D47 D72 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2019-09-09
New Economics Papers: this item is included in nep-des and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.economics.utoronto.ca/public/workingPapers/tecipa-644.pdf Main Text (application/pdf)

Related works:
Working Paper: Monotonic Norms and Orthogonal Issues in Multidimensional Voting (2021)
Journal Article: Monotonic norms and orthogonal issues in multidimensional voting (2020)
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:tor:tecipa:tecipa-644

Access Statistics for this paper

More papers in Working Papers from University of Toronto, Department of Economics 150 St. George Street, Toronto, Ontario.
Bibliographic data for series maintained by RePEc Maintainer ().