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Essentiality and Convexity in the Ranking of Opportunity Sets

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  • Matthew Ryan

    (School of Economics, Auckland University of Technology, NZ)

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 indifference 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.

Suggested Citation

  • Matthew Ryan, 2016. "Essentiality and Convexity in the Ranking of Opportunity Sets," Working Papers 2016-01, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:201601
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    References listed on IDEAS

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    7. V. Danilov & G. Koshevoy & E. Savaglio, 2015. "Hyper-relations, choice functions, and orderings of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 51-69, June.
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    Cited by:

    1. Rommeswinkel, Hendrik, 2011. "Measuring Freedom in Games," MPRA Paper 106426, University Library of Munich, Germany, revised 03 Mar 2021.
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    More about this item

    Keywords

    Opportunity set; freedom; essential alternative; essential element; abstract convex geometry.;
    All these keywords.

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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