Deterrence studies focusing on the certainty and severity of sanctions have been a staple of criminological research for more than thirty years. Two prominent findings from this literature are that punishment certainty is far more consistently found to deter crime than punishment severity, and the extra-legal consequences of crime seem at least as great a deterrent as the legal consequences
Further, as discussed here, harsher penalties can have paradoxical effects: they make juries more reluctant to convict, lowering the rate of conviction, and from the would-be criminal's side the reduced risk of conviction can outweigh the increased consequences.
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It does, but if people were that rational about risk decisions, nobody would buy lottery tickets.
On criminology, see e.g. Nagin & Pogarsky, Integrating Celerity, Impulsivity, and Extralegal Sanction Threats into a Model of General Deterrence: Theory and Evidence:
Further, as discussed here, harsher penalties can have paradoxical effects: they make juries more reluctant to convict, lowering the rate of conviction, and from the would-be criminal's side the reduced risk of conviction can outweigh the increased consequences.