This is a moderately interesting review article in the TLS about some books on euthanasia and the death penalty. I think they are rightly yoked together: my view, for what it is worth, is that each is a question of easy cases making bad law. One can readily see circumstances in which each seems like the most caring or moral or just outcome (as the case may be): euthanasia is topical and the examples well-known; and for capital punishment, consider the Nuremberg Trials. But just try coming up with a robust legislative structure that separates the easy cases from the hard ones ... most countries have given up on trying to do it with capital punishment, while the fashion seems to be to embark on the journey the other way with euthanasia.
All that is by the by for the purposes of this post. Instead I want to set up a thought experiment. Personal autonomy is of course the big difference between capital punishment and euthanasia: we are (in the easy cases) talking about someone who really, seriously, after thinking about it, wants to die. But what would you think of a law which, in specified cases (think of your own list e.g.: multiple murders, murder after acts of extreme sexual violence; murder in the course of treason) offered the convicted criminal the option of taking his life using whatever doctor-assisted mechanism is provided for euthanasia? He might well, in such cases, really, seriously, after thinking about it, want to die. He might also, unlike the terminally ill person, in some sense 'deserve' to die. Surely it would be no affront to his autonomy to give him the choice?
My initial reaction is that it would be wrong. But I'm having great difficulty putting a finger on why.
I suspect the main popular objection would be that it would be allowing criminals an easy way out. But was capital punishment - latterly intended to be swift and painless - ever viewed that way?