Closure and preferences

Christopher P. Chambers; Alan D. Miller; M. Bumin Yenmez

doi:10.1016/j.jmateco.2020.03.008

Closure and preferences

Christopher P. Chambers, Alan D. Miller, M. Bumin Yenmez

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).

Original language	English
Pages (from-to)	161-166
Number of pages	6
Journal	Journal of Mathematical Economics
Volume	88
DOIs	https://doi.org/10.1016/j.jmateco.2020.03.008
State	Published - May 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Closure
Kreps
Menu

ASJC Scopus subject areas

Economics and Econometrics
Applied Mathematics

Access to Document

10.1016/j.jmateco.2020.03.008

Cite this

@article{6af27112699449fb95ff5665dd931ab0,

title = "Closure and preferences",

abstract = "We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps{\textquoteright} axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).",

keywords = "Closure, Kreps, Menu",

author = "Chambers, {Christopher P.} and Miller, {Alan D.} and Yenmez, {M. Bumin}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = may,

doi = "10.1016/j.jmateco.2020.03.008",

language = "English",

volume = "88",

pages = "161--166",

journal = "Journal of Mathematical Economics",

issn = "0304-4068",

publisher = "Elsevier",

}

TY - JOUR

T1 - Closure and preferences

AU - Chambers, Christopher P.

AU - Miller, Alan D.

AU - Yenmez, M. Bumin

PY - 2020/5

Y1 - 2020/5

N2 - We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).

AB - We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).

KW - Closure

KW - Kreps

KW - Menu

UR - http://www.scopus.com/inward/record.url?scp=85083313848&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2020.03.008

DO - 10.1016/j.jmateco.2020.03.008

M3 - Article

AN - SCOPUS:85083313848

SN - 0304-4068

VL - 88

SP - 161

EP - 166

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

ER -

Closure and preferences

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this