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Two preference metrics provide settings for the study of properties of binary relations

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Abstract

The topological structures imposed on the collection of binary relations on a given set by the symmetric difference metric and the Hausdorff metric provide opportunities for learning about how collections of binary relations with various properties fit into the collection of all binary relations. For example, there is some agreement and some disagreement between conclusions drawn about the rarity of certain properties of binary relations using first the symmetric difference metric and then the Hausdorff metric.

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Notes

  1. All definitions the reader needs to follow the constructions are given in Sect. 2.

  2. I would like to thank Esteban Induráin for suggesting a second construction and the use of the Hausdorff metric in that construction.

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  1. Department of Economics, University of Connecticut, 327 Oak Hall, 365 Fairfield Way, Unit 1063, Storrs, CT, 06269-1063, USA

    Vicki Knoblauch

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  1. Vicki Knoblauch
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Correspondence to Vicki Knoblauch.

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Knoblauch, V. Two preference metrics provide settings for the study of properties of binary relations. Theory Decis 79, 615–625 (2015). https://doi.org/10.1007/s11238-015-9487-y

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  • DOI: https://doi.org/10.1007/s11238-015-9487-y

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