Common ordering extensions
AbstractThis article provides necessary and sufficient conditions for a collection of binary relations to have a common ordering extension. We also characterize the quasi-ordering that is obtained by taking the intersection over all these ordering extensions. Next, we consider the special case where the collection contains only two relations. In this special case, our necessary and sufficient conditions can be reformulated to include solely binary relations that are defined on a certain subset of the universal domain. The usefullness of our results are illustrated with several examples and we relate our findings to the results in the literature.
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Bibliographic InfoPaper provided by Ghent University, Faculty of Economics and Business Administration in its series Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium with number 09/593.
Length: 13 pages
Date of creation: Jun 2009
Date of revision:
Common ordering extension; consistency; Szpirajn’s lemma;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- D90 - Microeconomics - - Intertemporal Choice - - - General
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-07-28 (All new papers)
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