# Fair social orderings with other-regarding preferences

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## Abstract

We study the construction of social ordering functions in a multidimensional allocation problem where agents have heterogeneous other-regarding preferences (ORP). We show that there exists leximin social ordering functions satisfying equality and efficiency principles. When equality is defined as equality of *resources*, and ORP are only taken into account by efficiency principles, some of these social ordering functions are independent of the other-regarding part of preferences. When ORP are also taken into account by equality principles, results depend on the degree of resourcism of the social planner. If the planner still worries about equality of resources, some of the social ordering functions satisfying equality and efficiency remain independent of ORP. If the planner departs from a resourcist notion of equality, then social-ordering functions satisfying equality and efficiency must use information on the other-regarding part of preferences.

## Notes

### Acknowledgments

We thank François Maniquet, Marc Fleurbaey and John Weymark, as well as two anonymous referees for useful comments and discussions. Earlier versions of this paper were presented at several conference and workshop including the 2012 Poresp Workshop on well-being measurement with ORP, the 2013 ECORE summer school and the 2014 Winter School on Inequality and Social Welfare Theory. We thank Koen Decancq, Georg Kirchsteiger, Erwin Ooghe, Alessandro Sommacal, Frank Riedel, Claude d’Aspremont and other participants to these events for their questions and suggestions. Special thanks go to user203787 on http://math.stackexchange.com whose answer to a question helped to simplify the proof of Proposition 1. Fundings from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 269831 and from the Fond National de la Recherche Scientifique (FNRS, Belgium, mandat d’aspirant FC 95720) are gratefully acknowledged.

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