Today we discussed criminal trials from the juror's point of view. We decided, after some discussion, that the worst thing would be to convict someone who was actually innocent. We know from the Innocence Project that an unacceptably high proportion of people in prison are probably innocent. We set up a decision tree with branches Convict Innocent, Acquit Innocent (the worst and best outcomes) in a probability fork with u being the probability of CI and (1-u) the probability of AI, and the "for certain" branch of the tree being Acquit Guilty. After some discussion we decided on something like u=0.o1 which would mean that 99% of people sent to prison would actually be guilty (assuming we can evaluate that probability as a juror). With a loss of 0 for AI and 1000 for CI, we found that the loss for AG would be 10 to make us indifferent between the two branches.
We also discussed the case of Convict Guilty, and although some thought that AI would personally be better than CG (both correct decisions), this didn't seem to hold up when we replaced AG with CG in the decision tree we drew. CG for certain seemed better than CI with probability even as small as 0.001.
We also discussed whether the seriousness of the case and the harshness of the punishment should not also change our losses. Surely, some thought, the penalty for a traffic ticket is not as onerous a penalty as 20 years in prison for a serious crime, if the person accused were actually innocent, and the death penalty is even more unacceptable if the accused were actually innocent (even though Vermont doesn't have the death penalty, a recent Vermont jury did give the death penalty in a federal case, so it's not entirely moot even for Vermonters). So, the loss for CI ought to be larger if the penalty is more serious, some said. One student would never give the death penalty...for that student, the loss is effectively infinite.
The next several classes will be devoted to discussing the practice problems for the second test. We will pick up the juror discussion again after the test.
2 comments:
I seriously can't believe that its possible to achieve a probability .99 (all the time) that a person sent to prison to be actually guilty. If there is such a high standard of evidence required to convict someone, then the criminals often be released and commit those crimes again. The smart ones will keep doing it again and again, the others will keep committing crimes until such a high probability to convict is reached, which is absurd in my opinion.
I chose .90 probability required to convict him/her because it seemed more realistic. The justice system isn't entirely perfect, but its a system that works to capture criminals.
The only way in my opinion to decrease the number of innocent people in prison is to invest in education, reduction/elimination of poverty, rehabilitation of criminals, with particular focus in ethics and morals. This would reduce prison population, and lower the number of innocent people but not necessarily the percentage of them.
The other way that will NOT work in my opinion is to increase the probability of which a person is convicted guilty. To achieve such a high standard, would require a governmental agency to track and monitor everyone in the united states all the time, so that when a crime does occur we can convict with certainty. [Note: this is possible to implement today].
I am not sure if there is another way to increase the probability of which a person can be convicted guilty.
Tenzin raises some interesting questions. Is it possible in a trial to raise the posterior probability of guilt to at least 0.99? I think that it is, but I could be wrong, and we'll have plenty of opportunity to discuss this after the test. Maybe Tenzin is right, and if he is, it raises serious problems about our criminal justice system.
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