Economics at your fingertips  

A characterization of the generalized optimal choice set through the optimization of generalized weak utilities

Athanasios Andrikopoulos ()

Theory and Decision, 2016, vol. 80, issue 4, No 5, 621 pages

Abstract: Abstract It often happens that a binary relation R defined on a topological space $$(X,\tau )$$ ( X , τ ) lacks a continuous utility representation; see, e.g., (Peleg, in Econometrica 38:93–96, 1970, Example 2.1). But under an appropriate choice of a second topology $$\tau ^{*}$$ τ ∗ on $$(X,\tau )$$ ( X , τ ) , the existence of a semicontinuous utility representation on the bitopological space $$(X,\tau ,\tau ^{*})$$ ( X , τ , τ ∗ ) can be ensured (see Remark 1 in the text). On the other hand, the traditional notion of weak utility representation as defined by Peleg (Econometrica 38:93–96, 1970) cannot be used to characterize the generalized optimal choice set, which requires binary relations that allow cycles. The main result in this paper states that for any generalized upper tc-semicontinuous, separable, pairwise spacious and consistent binary relation R defined on a bitopological space $$(X,\tau _1,\tau _2)$$ ( X , τ 1 , τ 2 ) and any subset D of X, there exists a utility function which characterizes the generalized optimal choice set of R in D in terms of the maxima of this function.

Keywords: Condorcet winner; Generalized optimal choice set; Weak utility function; Bitopological space (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
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:

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/11238/PS2

DOI: 10.1007/s11238-015-9517-9

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 () and Springer Nature Abstracting and Indexing ().

Page updated 2021-06-18
Handle: RePEc:kap:theord:v:80:y:2016:i:4:d:10.1007_s11238-015-9517-9