The state doesn't determine such: unanimous juries of our citizen peers do. The question of someone's criminal guilt or innocence isn't decided by administrative fiat, it's applied consistently with majoritarian principles and standards of community conduct.
The potential of some vanishingly few innocents being put to death is an appropriate price to pay for maintaining the retributive principle that protects and maintains the social contract.
So you’d be okay with a racist Southern jury condemning a Black man to be condemned to death or lifetime slave labor for some minor offense? After all, that could conceivably count as “maintaining the retributive principle that protects and maintains the social contract,” and examples of this exact phenomenon existed and persist in the South to this day.
No, of course not. Firstly, a racially segregated jury is hardly valid in that it isn't constituted "of one's peers." Secondly, a retributive theory of justice demands punishments that are proportionate to the crime. "An eye for an eye" means minor offenses receive the most minor punishments, while more severe crimes get harsher ones. Theories of punishment based on criminal deterrence or rehabilitation cannot actually answer this question of how severe sentences should be. In an ideal system, legislatures set bounds for what the prescribed criminal punishments ought to be and judges and juries dole out specific sentences considering any mitigating or aggravating circumstances.
But the 'hardly valid' jury can still sentence someone to death.
This is the problem I have with the death penalty. People could be innocent, no matter how 'air tight' the evidence is against them. Unless you literally catch Osama bin-Laden it's not morally right.
Also I love how 'pro-life evangelicals' support the death penalty.