Orderings of Opportunity Sets
AbstractWe consider an extension of the class of multi-utility hyper-relations, the class of semi-decent hyper-relations. A semi-decent hyper-relation satis es monotonicity, stability with respect to contraction, and the union property. We analyze the class of semi-decent hyper-relations both associating them to an appropriate class of choice functions and considering decomposition of a decent relations via elementaryones. Doing so, we consider images in the set of choice functions of three subclasses of semi-decent hyper-relations: the decent hyper-relations, the transitive decent hyper-relations , and transitive decent hyper-relations which satisfy the condition LE of lattice equivalence. We prove that the image of the set of decent hyper-relations coincides with of the set of heritage choice functions; the image of the set of transitive decent hyper-relations coincides with the set of closed choice functions; the image of the set of transitive decent hyper-relations which satisfy the LE coincides with the set of Plott functions. We consider, for each of the above subclasses of hyper-relations, the problem of the decomposition of a given hyper-relation into elementaryones, namely the representation of a given hyper-relation as the intersection of elementaryones.
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Bibliographic InfoPaper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 282.
Length: 17 pages
Date of creation: Dec 2012
Date of revision:
Hyper-relations; opportuntiy sets; preference for flexibility.;
Other versions of this item:
- Vladimir Danilov & Gleb Koshevoy & Ernesto Savaglio, 2012. "Orderings of Opportunity Sets," Department of Economics University of Siena, Department of Economics, University of Siena 660, Department of Economics, University of Siena.
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- repec:hal:journl:halshs-00203346 is not listed on IDEAS
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