Regardless of their views on capital punishment most people desire it to be centred on due process and fairness. But a software experiment, by showing that the likelihood of execution of people on death row can be predicted to high accuracy, paradoxically suggests a great degree of arbitrariness in how the death penalty is applied in the US. A death sentence is essentially a lottery ticket: the condemned will be executed with a certain probability and otherwise suffer a long and uncertain imprisonment. But different convicts get different probability tickets, even when the legal system and all criminal circumstances are the same.
The researchers took data such as state, sex, race, year of birth, years of conviction, prior convictions etc. for 1000 convicts, half of which had been executed. This was used to train an artificial neural network, a standard machine learning technique. The network was trained to decide whether a person was executed or not from the given data, and whenever it decided wrong it was adjusted towards the correct answer. After enough training it not only accurately (90% right) predicted the fate of the convicts it had been trained on, but also as accurately on 300 convicts it had never encountered before. Their paper describing the method can be found here.
That the network could predict who would be executed is problematic from a legal standpoint since the legal system aims at being consistent and fair. Once someone has been sentenced their fate, whether it is fundamentally fair or not, should not be due to arbitrary personal factors (the data included) that are independent from the substantive characteristics of their crimes (which were not included). That the link may not follow an (to a human) easily seen pattern does not remove the causal effect.
Apparently recent results show that the situation is even worse (I say apparently, since this information come merely from the news story, I have not found any published paper yet; there is some risk of this being "science by press release"). The researchers tried leaving out one factor at a time when they trained the network, examining which were most important for predicting outcomes. Race may increase the risk of being sentenced, but once on death row it had little effect. Gender was a strong factor: women are rarely executed. The strongest factor was educational level: the more years in high school, the better the chances of not being executed. Most likely this corresponds to being able to manage an appeals process. Whether it is just education or some deeper factor such as general intelligence is not possible to tell, but clearly it produces an unfair situation. Education is not a relevant reason for a legal system to commute a punishment.
For an opponent of capital punishment there are of course much stronger reasons against it than just this particular unfairness. For a supporter it poses a subtle problem, since it is very unlikely that it can be removed without losing due process or fairness – it is after all the ability to appeal that is the crucial factor.