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There is controversy on whether there are a few percents of innocent people in US jails or much less.

For example according to the Innocent project

Q. How many innocent people are there in prison?

A. We will never know for sure, but the few studies that have been done estimate that between 2.3% and 5% of all prisoners in the U.S. are innocent (for context, if just 1% of all prisoners are innocent, that would mean that more than 20,000 innocent people are in prison).

But also

That would make the error rate [in felony convictions] .027 percent—or, to put it another way, a success rate of 99.973 percent.

--The innocent and the Shammed

Is there a statistically valid study on wrongful convictions that can settle the debate?

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Obviously the rate of wrongful convictions is hard to estimate because a conviction (at least in theory) follows a rigorous examination of the evidence by a court. So in order to classify a conviction as wrongful, researchers need evidence that's significantly stronger than the evidence that was examined by the convicting court. There aren't many opportunities to get hold of such evidence in a systematic way.

However, post-conviction DNA testing provides such evidence. DNA testing only became reliable and cheap enough to be routinely used in criminal investigations in the 1990s, so there was an opportunity to re-examine convictions in which DNA evidence had not been used.

The paper "Post-Conviction DNA Testing and Wrongful Conviction" by Roman, Walsh, Lachman and Yahner, summarizes the results from an important study based on post-conviction DNA testing. I'll quote from the executive summary:

In Virginia, a cohort of 634 cases of sexual assault and/or homicide dating from 1973 to 1987 was discovered to have retained physical evidence. Since most state legislation that requires evidence storage was enacted in the post-DNA era, it is likely that many states have not preserved physical evidence for cases from the pre-DNA era. Therefore, the evidence in the Virginia cases provides a unique opportunity to determine how often DNA testing can be used to identify wrongful convictions. The results can be generalized (with caveats) because the physical evidence was retained for reasons unrelated to the case outcome, and the cases were assigned to the serologist who retained the evidence in a way that did not introduce bias.

Of the cases originally reviewed (more than 534,000), approximately 3,000 had retained physical evidence; in 2,100 of those cases a suspect was identified; and 740 cases had at least one suspect convicted of a felony. Of those, 634 cases with 715 convictions (62 cases had multiple suspects) were NIJ eligible based on crime type (homicide, sexual assault) and a conviction.

DNA testing produced a determinate outcome for 230 of these cases, in which there were 250 convicted offenders. In 56 of those convictions the convicted offender was eliminated as the source of DNA evidence, and for 38 convictions that elimination supported exoneration.

Given the potential inaccuracy of an estimate of any rate of wrongful conviction, we provide two statistics as an alternative, both based on the actual numbers observed in this data:

1) The rate at which convictions for serious person crimes and retained evidence yielded a DNA profile and the convicted offender was eliminated as the source (56/715 or 7.8 percent); and

2) The rate at which convictions for serious person crimes and retained evidence yielded a DNA profile and the convicted offender was eliminated, and that elimination appears to be probative evidence that supports exoneration (38/715 or 5.3 percent)

You should read the whole paper for details and caveats. But the results seem to be in line with the figures given by the Innocence Project.

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  • In England (and I suspect even more so in the USA) a conviction rarely follows any examination of the evidence because most convictions follow a plea of guilty. I also guess it would be unsafe to assume that a plea of guilty is equivalent to guilt in a system with extensive plea bargaining. That doesn't mean your answer is wrong, just a caution. Also sexual offences and homicide are a rather small and skewed sample of the whole. – Francis Davey Mar 24 '17 at 17:01

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