Dominance Relations Among Standardized Variables
研究离散随机变量之间的随机占优关系，在共同整数域上得到新理论结果，并简化了现有证明。对任何阶占优准则，被占优变量等于占优变量加上扰动项，并描述了不同占优准则下扰动项的性质。
This paper examines stochastic dominance relations among discrete random variables defined on a common integer domain. While these restrictions are minimal, they lead both to new theoretical results and to simpler proofs of existing one. The new results, obtained for dominance criteria of any degree, generalize an SSD result of Rothschild-Stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms. If the variables are comparable under FSD the perturbations are downward shift terms, while under SSD (TSD) all but two (three) of the perturbations are zero mean disturbance terms (noise). Under SSD the remaining perturbations are shift terms and under TSD noise and shift terms. However, under either SSD or TSD these remaining terms are identically zero if the variables to be compared have equal means. The paper also finds new proofs of well known results relating dominance criteria to preferences.