I'll copy what I said on another thread.
The biggest problem with death penalty is the possibility for someone to be executed for a crime they did not commit, due to bad evidence, biases/prejudices, being framed or set up, etc. And there is the concern to be made of allowing governments as corrupt as they tend to be the legal power to execute people as need be. Though, being able to imprison people for life could be considered a concern for a similar reason. Political dissidents and the like get executed a lot in the authoritarian nations that exist (like China whose total number of executions is kept a secret.)
I think both can be quite punishing but it makes you think when people choose death rather than going to prison which one is actually "worse." I'm not sure what the answer would be if you asked the majority of people in the world whether they would prefer death or life imprisonment. The quality of the prisons is something to take into account I suppose, like prisoners in some countries have more rights and "luxuries" than in other countries.
The death row in America at least is quite flawed anyway as many people will remain on death row for decades before being executed, or eventually having the death penalty converted to a life sentence instead. And there are logistical problems with the manufacturers of the drugs for lethal injection refusing to supply those drugs anymore to states that still have the death penalty. I think there are some similar problems in other countries.
There is also the matter of the philosophy behind why prisons exists. Whether the purpose is to keep people safe from predators, so they are taken out of society, in whatever way that means (imprisonment or death) or whether it is about punishing the person who committed the crime. I care more so about the first reason and so which punishment is actually more punishing is less relevant in that instance.
I do think people in prison should be given the option of euthanasia. Maybe it is only given after a certain point of time served in their sentence. I don't think it is likely to realistically happen any time soon, though.
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Philosophically I can understand and agree with the desire for the death penalty for perpetrators of very heinous crimes without any justification, in practice I think the risks that come with it are too great. I think a life sentence is a bad enough punishment.