On the Difficulty of Combining Actual and Potential Criteria for an Increase in Social Welfare

This paper examines a combination of a quasi-ordering on set of alternatives (interpreted as a criterion for an increase in actual social welfare) and an extension of this quasi-ordering to the power set of this set (interpreted as a criterion for an increase in potential social welfare). The main result of this paper is that, in order for such a combination to be transitive, it is necessary and sufficient that the subset to which it is applied is such that the extension encompasses the original criterion. When applied to the standard Pareto quasi-ordering and its extension defined by the Chipman-Moore (1971) - Samuelson (1950) quasi-ordering, and under standard assumptions on the economic domain, this result is shown to imply Gorman’s (1955) conjecture for the transitivity of the Compensation criterion à la Kaldor-Hicks-Scitovsky.