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There’s also another aspect: whether it’s one life sentence or 5 consecutive might make very little difference. Since prisons in US are big business nobody deals in short sentences. Rehabilitation or deterrence are not the goals, so of course the strategy won’t have the effect you imagine.

When punishments are so disproportionately high a good chunk of the ofenders will stop caring. The preventative effect is gone, it’s more an incentive to escalate the crime to a level where it matches the punishment.