On bounded dominance criteria

A well-known criterion to make heterogeneous welfare comparisons is Atkinson and Bourguignon's sequential generalized Lorenz dominance (SGLD) criterion. Recently, Fleurbaey, Hagneré and Trannoy convincingly argue that it contains unreasonable household utility profiles and suggest to put (lower and upper) bounds on the needs of the different household types. First, we generalize Atkinson and Bourguignon's SGLD criterion, by introducing lower bounds directly into the household utility profiles. Second, we propose a new SGLD criterion by introducing upper bounds in a similar way. Third, we impose lower and upper bounds simultaneously and obtain a criterion which is intermediate between Ebert's equivalence scale weighted approach and Atkinson and Bourguignon's SGLD approach.