there are majorities who believe that the death penalty does not deter murders...and that innocent people can be convicted.
Think about it...only a rational person would be deterred from committing murder by the death penalty...virtually none of the perpetrators would be called 'rational'...either they have severe mental illness, or the crime is one of passion...plus, the death penalty doesn't make anything "right".
Link: https://www.pewresearch.org/fact-tank/2021/07/19/10-facts-about-the-death-penalty-in-the-u-s/