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This paper examines egalitarian evaluations of streams of (possibly different dimensional) utility vectors of generations. We propose three infinite-horizon variants of the critical-level leximin principle: the critical-level leximin social welfare relation (SWR),
the critical-level leximin overtaking SWR, and the critical-level leximin catching-up SWR. It is shown that the critical-level leximin SWR is characterized by five axioms: finite anonymity, weak existence of critical levels, existence independence, strong Pareto, and Hammond equity. Further, the critical-level leximin overtaking and the critical-level leximin catching-up SWRs are characterized by adding consistency axioms. We prove these results by showing the general result that three of the five axioms: finite anonymity, weak existence of critical levels, and existence independence imply that an evaluation within a generation must be extended between generations. We also evaluate the three SWRs by using population ethics axioms.
