Decisions under uncertainty: expectations, capital and an unfortunate current example

This is not a political site and we are not interested in making political or moral statements.  But we are deeply interested in how people and societies make decisions under uncertainty.

Theoretically one needs to account for both the expected value of the strategy and some cost of carrying uncertainty, as long as it persists.

What is the value in an execution?  Accepting the eye-for-eye 'logic' for a moment we have:

• Pright = probability guilty verdict is correct
• Cost of original crime = -1.0
• 'Value' of imprisonment to date = +0.25  (22 yrs)
• Incremental value of immediate execution =   0.50 
• 'Value' of imprisonment for rest of life = ?  = 0.25?
• Cost of being wrong and executing =  large negative (Let's be generous to the eye-for-eye perspective and call it -0.50 and neglecting the immense  societal costs.  We will also neglect the societal costs- if any- of life imprisonment when death-penalty was 'justified'.)

So for the execution strategy
      Expected value =  -0.75 (current state) + Pright*(0.50)+Pwrong*(-0.50)

For the don't execute strategy
      EV = -0.75 +0.25

So, to make execution a good decision (better expected outcome) we need
     -0.75+Pright(0.50)+(1-Pright)*(-.50) > -0.5    

                                            or    Pright>75%

So even on an expected basis we need to be very certain the verdict is correct.  Moreover, if one introduces the a more realistic assessment of the damage to the justice system and society of being wrong, the need for certainty will be greatly increased.

For instance:
if Cost of being wrong and executing = -2.0 we need to be 90% certain.

When the cost of uncertainty 'capital' (say, proportional to the standard-deviation of the payoff distribution)-- which will accrue until conclusive evidence is discovered is brought into the picture-- the demands on Pright will be higher still.

So even if one accepted the death penalty from a moral perspective, given the dubious nature of the legal case, it seems that a very bad decision was made.