Fatal flaws

A recent Associated Press story told of some studies that show that the death penalty has a strong deterrent effect. Murder rates go down when the death penalty is relatively swift and sure, these statisticians say. Their findings are very disagreeable to death penalty opponents, some of whom quarrel about the statistical methods.

My off-the-cuff response is that capital punishment is quite likely to deter premeditated murder and even some "heat-of-the-moment" homicides. So it seems plausible that such a policy saves lives.

Yet, there is another issue. Is it OK to sacrifice the lives of some innocent persons in order to help spare the lives of others? Some may say that, though capital punishment errors may occur, such miscarriages of justice are relatively rare and that the risk of such error is a necessary societal evil.

Before giving some back-of-the-envelope numbers, a remark: The fact that an error rate is low means, in this case, that the chance that a randomly selected Death Row inmate is innocent is low; that fact does not mean that the chance of an innocent person being executed is low. That chance rises with the number of inmates.

So here goes:

Of 300 persons sentenced to die in Illinois between 1977 and 2000, 13 were exonerated as wrongfully convicted (that is, courts found that a reasonable doubt existed as to each one's guilt; in some cases, there was no doubt at all as to innocence). Of the 300, 12 were executed. [Source: The Death Penalty on Trial by Bill Kurtis, Perseus Books (PublicAffairs unit), 2004.]

In other words, the Illinois error rate was 13/300 = 4.3%. Fearing that there might be more innocent men on Death Row, then-Governor George Ryan pardoned some inmates and commuted the sentences of all the others to life terms. Hopefully the 12 persons who had died since 1977 had all been guilty, Ryan said.

We can get an idea about his concerns by using the Poisson formula, which is applicable to sufficiently large populations. A number near 300 (actually 287 once the 13 exonerated are excluded) can qualify for the Poisson method. What is the probability that none of the 287 is innocent? The probability is simply exp(minus error rate times sample) = exp(-0.043x287) = exp(-12.341) = 4.369 x 10^-6. Turned around, that means that Ryan faced a probability of 99.99999563 percent that Illinois either had since 1977 or would execute someone then on Death Row wrongfully.

Still, the Poisson method can't be used for a small sample size, such as the 12 people executed in Illinois since 1977.

But there is one state that has carried out a sufficient number of executions to warrant use of the Poisson method: Texas executed 154 people between 1995 and 2000, with 39.4% of Death Row inmates put to death in that period. A 4.3% error rate would give an expected value of 6.622. With that number, the probability that no innocent person was executed during George Bush's governorship is less than 1%. Put another way, the likelihood of a wrongful execution is 99.867%. [Source of input data: Bureau of Justice Statistics as cited in The Contradictions of American Capital Punishment by Franklin E. Zimring, Oxford University Press, 2003.]

But suppose Texas doesn't have such a high error rate in capital cases. Somehow it is quite difficult to believe that the Texas justice system is far, far superior to the Illinois system. A lower limit of 1% in Texas seems reasonable. Even so, we have exp(-1.54) = 21.438% probability that no one was wrongly convicted, which is to say a 78.56% probability that Texas executed at least one innocent person during the 5-year interval.

No other state has a comparable number of executions during that period. However, the total number of executions nationwide was 2899 during that five years [Source: Bureau of Justice Statistics in Zimring.] An error rate of 4.3% yields exp(-124.657) = 7.28 x 10^-55, which is a fantastically low number, meaning that the probability no one was wrongly executed is effectively zero. At a 1% error rate, the probability no one was wrongly executed is 2.569 x 10^-13, which is also effectively zero.

That is, it is virtually certain that one or more innocent people were executed in the United States between 1995 and 2000.

You may recall that George Bush was the governor who pushed through the vast speedup in executions in Texas.

Which brings us to the matter of military tribunals for unlawful enemy combatants. What hope is there for a low error rate and no wrongful executions? Hard to say. However, bear in mind that the GOP has made the standards of evidence much lower than the American norm for such captives. When, for example, confessions extracted by dubious means out of the presence of counsel or international observers are admissible evidence one should anticipate that innocent people will be convicted and that some may be executed.