We establish mathematical equivalence between independence of irrelevant alternatives and monotonicity with respect to first order stochastic dominance. This formal equivalence result between the two principles is obtained under two key conditions. Firstly, for all , each principle is defined on the domain of compound lotteries with compoundness level . Secondly, the standard concept of reduction of compound lotteries applies. We establish mathematical equivalence between independence of irrelevant alternatives and monotonicity with respect to first order stochastic dominance. This formal equivalence result between the two principles is obtained under two key conditions. Firstly, for all , each principle is defined on the domain of compound lotteries with compoundness level . Secondly, the standard concept of reduction of compound lotteries applies.
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