Virtually any method is fine with me.
Actually if you wanna get right down to it I think it should be possible to choose your own method of death, the same as getting to choose a last meal, because I mean you're gonna die and it's gonna be painful to some degree anyway but if you wanna go out with some style or some dignity then i think that should be an option.
However, this would present all sorts of issues if you let people pick whatever they wanted so you'd have to give them limited options like lethal injection, hanging, the electric chair, death by firing squad, things like that you know.
That's not very practical though so I'm going with hanging, the electric chair, firing squad, and lethal injection.
However, ideally speaking that is, for the worst of criminals facing the death penalty I think it would be a much better idea to just let them kill each other off. Why? Because this way an innocent person doesn't have to kill someone regardless if that person is guilty. Obviously I'm talking about the executioners here.
People bad enough to warrant the death penalty are usually people who've killed a lot of other people directly or indirectly. Or they could be traitors to their country/government. And that probably did lead or could lead to a lot of of their countrymen getting killed at some point - even if they didn't directly kill anyone, blood would still be on their hands, basically.
But anyway, the only real issue (as far as justice being served) with this is that there's going to be one left standing and if they're not going to get any reward out of surviving then none of them would be prompted to fight in the first place. Because why? So they could go back to a maximum security prison and rot in a hole for the rest of their days? Ha ha, no.
So to do something like this, you'd have to bait the inmates with a reward - something worth fighting for other than just surviving. Which can cause issues with the closure that family/friends of the inmates victims need.
On the other hand, this wouldn't mean they'd get off scott free or anything, he'd be forced to fight again for the same stakes. Eventually, someone more badass will come along and they'll die so, if you look at it that way then it could work.
So in a manner of speaking... Deadman Wonderland but with less of the bullshit like the blood powers and the inmates being a source of violent entertainment for the masses. Just a straight-up fight for your life, if you win you get some rewards and next time executions come up you do it all over again. And also it wouldn't be televised to anyone except family members of the inmates or family of the victims of the inmates - if they so choose to watch it.
Really I think it would better just to let them kill themselves off that way by dangling a carrot in front of them and letting them fight over it. Whoever is the last alive gets the carrot. I just think it's fitting really.
Also though, this would be optional. You could choose a standard method of execution if you just wanna get it over with, as opposed to fighting it out. But if you did that most would probably figure out the risk-reward factor quickly and decide the minor reward isn't worth the possibility of dying brutally when they can choose a more peaceful death, even if it mean the only option is death.
But that's ideally speaking, I just think it's better to let them kill themselves off is all. Better than making innocent people take a life, even if that life is guilty, in my humble opinion.
I mean, that's why some lethal injection methods are set up to where no one knows who is shooting the person up with the lethal injection or not. Takes away some of the guilt.
So why not come up with a way to eradicate the need for that guilt altogether?
That or we penal colony their sorry asses and let them fend for themselves. If they survive, good for them, if they die then that's fine too. But they'd never get off the colony is the point, dead or alive. But you'd have to find somewhere to put them first, somewhere where you'd have to be a suicidal fool to try and escape.
Well anyway, that about sums it up for me. Guess I'm a tad fickle on the subject when it comes to method.