Variable population egalitarian ethics and the critical-level: A note

This paper explores the introduction of a variable critical-level in a variable population context. We focus the attention on the "Critical- Level Egalitarian Ruleî, 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 small 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 rule. This problem disappears when a weak monotonicity condition is required.