Lexicographic expected utility without completeness
Dino Borie ()
Theory and Decision, 2016, vol. 81, issue 2, 167-176
Abstract Standard theories of expected utility require that preferences are complete, and/or Archimedean. We present in this paper a theory of decision under uncertainty for both incomplete and non-Archimedean preferences. Without continuity assumptions, incomplete preferences on a lottery space reduce to an order-extension problem. It is well known that incomplete preferences can be extended to complete preferences in the full generality, but this result does not necessarily hold for incomplete preferences which satisfy the independence axiom, since it may obviously happen that the extension does not satisfy the independence axiom. We show, for incomplete preferences on a mixture space, that an extension which satisfies the independence axiom exists. We find necessary and sufficient conditions for a preorder on a finite lottery space to be representable by a family of lexicographic von Neumann–Morgenstern Expected Utility functions.
Keywords: Lexicographic Expected utility theory; Order extension; Preorder (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (2) Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s11238-015-9523-y Abstract (text/html)
Access to full text is restricted to subscribers.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:kap:theord:v:81:y:2016:i:2:d:10.1007_s11238-015-9523-y
Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/11238/PS2
Access Statistics for this article
Theory and Decision is currently edited by Mohammed Abdellaoui
More articles in Theory and Decision from Springer
Bibliographic data for series maintained by Sonal Shukla ().