Can a tiny gain to sufficiently many well-off justify imposing a much larger sacrifice on the worst-off? We show that if one answers negatively to such a question and endorses replication invariance, one is forced to accept the maximin principle and give full priority to the worst-off even when a tiny gain to the worst-off imposes a substantial sacrifice on arbitrarily many well-off. If one dislikes this consequence, one faces a real dilemma in choosing between the tyranny of aggregation and the tyranny of non-aggregation.
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