# First-order dominance: stronger characterization and a bivariate checking algorithm

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## Abstract

How to determine whether one distribution first-order dominates another is a fundamental problem that has many applications in economics, finance, probability theory, and statistics. Nevertheless, little is known about how to efficiently check first-order dominance for finite multivariate distributions. Utilizing that this problem can be formulated as a transportation problem with a special structure, we provide a stronger characterization of multivariate first-order dominance and develop a linear time complexity checking algorithm for the bivariate case. We illustrate the use of the checking algorithm when numerically assessing first-order dominance among continuous bivariate distributions.

## Keywords

Multivariate first-order dominance Usual stochastic order Characterization Network problem Checking algorithm## Mathematics Subject Classification

60E15 90C08 91B82## Notes

### Acknowledgements

We are grateful to Bettina Klinz, the two anonymous referees, and the associate editor for valuable comments and suggestions. Furthermore, we wish to thank the participants of the 12th International Conference on Computational Management Science, 2015, in Prague and the participants of the Conference on Economic Design 2015, Istanbul, July 2015, for their helpful discussions.

## Supplementary material

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