# How to rank rankings? Group performance in multiple-prize contests

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## Abstract

When groups of individuals compete in several multiple-prize contests, the performance of a group is a vector of ordered categories. As the prizes are aimed at ranking the participants, group performances are not trivially comparable. This note provides a theoretical discussion on how to rank group performances. In order to do so, I draw from the parallel that this problem has with the formally similar problem of measuring inequality. I describe three alternatives that generate partial orders for group performances. I define partial orders based on the first- and second-order dominance, two classes of performance measures, and two sets of basic transformations, and I prove equivalence theorems between them. I apply these theoretical results to discuss several sports ranking problems.

## Notes

### Acknowledgements

I would like to thank Juan Pablo Torres for his valuable feedback. I acknowledge financial support from the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo.

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