The Mass Transfer Approach to Multivariate Discrete First Order Stochastic Dominance: Direct Proof and Implications

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A fundamental result in the theory of stochastic dominance tells that first order dominance between two finite multivariate distributions is equivalent to the property that the one can be obtained from the other by shifting probability mass from one outcome to another that is worse a finite number of times. This paper provides a new and elementary proof of that result by showing that starting with an arbitrary system of mass transfers, whenever the resulting distribution is first order dominated one can gradually rearrange transfers, according to a certain decentralized procedure, and obtain a system of transfers all shifting mass to outcomes that are worse.
TidsskriftJournal of Mathematical Economics
Udgave nummer6
Sider (fra-til)1222–1228
StatusUdgivet - nov. 2010
Udgivet eksterntJa


  • Multidimensional first degree distributional dominance
  • The usual stochastic order
  • Multivariate majorization
  • Generalized equivalence result