Maybe? I'm not sure the analogy helps here, as it seems unclear that prisons are an effective way to discourage crimes.
This here govt website suggests is the act of being caught that is the major deterrent to crime, not the severity of the punishment https://nij.gov/five-things/pages/deterrence.aspx
Original source: http://www.jstor.org/stable/10.1086/670398?seq=1#page_scan_t...