Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/242540
Authors: 
Ryan, Matthew
Year of Publication: 
2016
Series/Report no.: 
Economics Working Paper Series No. 2016/01
Abstract: 
This paper studies the essential elements (Puppe, 1996) associated with binary relations over opportunity sets. We restrict attention to binary relations which are re?flexive and transitive (pre-orders) and which further satisfy a monotonicity and desirability condition. These are called opportunity relations (ORs). Our main results axiomatically characterise two important classes of ORs: those for which any opportunity set lies in the same indiĀ¤erence class as its set of essential elements the essential ORs; and those whose essential element operator is the extreme point operator for some abstract convex geometry (Edelman and Jamison, 1985) ?the convex ORs. Our characterisation of convex ORs generalises the analysis in Klemisch-Ahlert (1993), who restricts attention to a particular subclass of ACGs known as convex shellings. We present an example which suggests that this latter class is restrictive ?there are ACGs which are not convex shellings but which are associated with plausible ORs.
Subjects: 
Opportunity set
freedom
essential alternative
essential element
abstract convex geometry
JEL: 
D60
D63
Document Type: 
Working Paper

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