HCOL 195 11/2/09

We decided to have the second test on Wednesday, November 18.

We then turned to the question of the death penalty, which although it is not allowed under Vermont state law, could conceivably be a problem for a Vermont jury which was convened in a federal capital case, as one Vermont jury recently was faced with this problem. I pointed out that a potential juror will be required to answer questions in vior dire, where each juror is questioned under oath about the case: Do you know the defendant or the victim, what have you heard about the case, can you render an impartial verdict, etc. In a capital case, you will also be asked whether you are opposed to the death penalty, and if you answer “yes,” then you will not be allowed to serve on that jury.

We then proceeded to consider a decision tree for a juror. This is a linked decision, so we need to have a second decision box if the jury decides to convict, since the second choice is “Death” or “Life in Prison.” See below for the general form of the tree, which we drew without many of the losses inserted.

We noted that each juror will have different losses for the outcomes. AI is clearly the best, with a loss of 0. It seems like we ought to assign some small loss to CG, Life, and since the scale is arbitrary, we assigned 1 for that case. We then considered what the loss should be for AG, and decided on 10 for this (although we also discussed 100; since we are illustrating the process, and everyone will come up with their own loss structure, we can use whatever will illustrate the process):

Determining loss for AG relative to CG, Life

Determining loss for CI, Death

We decided that convicting an innocent person and putting him in prison for life was pretty bad, and with a similar tree (not shown, sorry, I didn’t snap a picture of it), we settled on CI, Life=1000 for the loss. Then, we drew the above picture, and noted that CI, Death is worse (for the juror) than CI, Life. That means (if you believe it) that in the above trial decision, we should set p0 to some number less than 1, so the loss for CI, Death should be 1000/(1-p0) and will be larger than 1000. We then entered our losses, determined in this way, into the decision tree we had sketched before:

Death penalty decision tree

Because of the last observation, it’s clear that if we think that sending an innocent person to his death is worse than putting him in prison for the rest of his life, then (if we use decision theory) we will never decide on the death penalty, regardless of whether we personally approve of that penalty or are opposed to it.

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