Egalitarianism, Variable Population and Monotonic Critical Level

This paper explores the introduction of a variable critical-level in a variable population context. We focus the attention on the Critical- Level Leximin criterion, a social evaluation procedure which compares two social states as follows: (i) It reproduces the Leximin criterion when applied to vectors of identical dimension and (ii) otherwise, it completes the smaller one with so many times a variable critical-level as to make the two vectors equal in size and applies the Leximin criterion again. We prove that the use of a strict monotonic critical-level leads to the intransitivity of the social evaluation criterion. This problem disappears when a weaker monotonicity condition is required.