I do mot support the death penalty, leeneia, but this book will give some insight, I expect.

I am quite comfortable for Steve and others to think there are no good arguments in favour: it may just be a difference in terminology. I think that the arguments in favour of the death penalty need to be thought about seriously because it is a serious subject. Having thought about them I find them lacking and in the end they do not persuade me. Similarly the arguments opposed to the death penalty deserve to be treates seriously by those in favour of it, again because it is a serious subject that deserves being treated seriously.

There is a lot of heat on other threads about evidence. For this question you need to be thinking what you want to achieve and then see what the evidence is. I did a short adult education course on the topic a decade or so ago and as far as I understand it the evidence is compatible with my opposition to the death penalty.