Citation needed. From what I understand, 1) that theory is incorrect and the death penalty is not seen as a deterrent by potential future criminals (rather it may be the opposite) [citation coming]; and 2) Policymakers who say it is a deterrent are either lying or disinformed.

My understanding of the death penalty is that it is intended as violent punishment and is done gruesomely for the purposes of revenge. Read any thread online about a bad crime and you will see mobs of people calling for violent, public murders of the accused. It's human nature for a lot of people and something I think a civilized nation would immediately outlaw, especially ones that pride themselves on not doing "cruel and unusual punishment". I remember reading that the death penalty in the US doesn't fall under that category merely because of the 'and' clause and the relatively common nature of gruesome murders by the State in the US.

[citations]. It seems that states without the death penalty have lower murder rates, suggesting the opposite forces are true compared to your post (edit: i.e, it might even mean that a place with state-sanctioned/performed murder is more likely to have murders).

https://deathpenaltyinfo.org/deterrence-states-without-death...