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The prisoners dilemma and a fair justice system

The prisoners dilemma is probably the most well known product of game theory. Typically, the game is used to illustrate the difficulty of sustaining mutual cooperation. But, as the name may suggest, it also raises questions about justice and the legal system. A recent article in the economist suggested that power has swung too much in favour of the prosecution in the US justice system. The prisoners dilemma can help us understand how easily this can happen.
       Suppose that Fred and William are arrested by the police in regard to a serious crime. The two are put in separate rooms and questioned. There is clear evidence that they committed a minor crime but the evidence regarding the serious crime is weak. The basic options open to the two suspects are to deny the serious crime or confess but blame the other suspect. If they both deny then they will receive one year in jail for the minor crime. If both confess then they will receive ten years in jail for the serious crime.
      The crucial thing is what happens if one confesses and the other denies. The police offer a deal: If Fred confesses and William does not then Fred walks away without a jail term. A similar deal is offered to William. Putting this together we end up with the game depicted below. We see that, no matter what William does, Fred is better off confessing. Same goes for William. The prediction, therefore, is that both Fred and William will confess. 
 
        For the police and society this looks like a good outcome - we get a conviction. Note, however, that the story above says absolutely nothing about whether Fred and William are actually guilty of the serious crime. They may not be guilty! The crime may have been committed by someone else! In this case confession does not look such a good outcome.
        At this point you might argue that an innocent person would never confess, because of psychological costs not captured in the simple game above. We know, however, that may innocent people do confess. You might also argue that the police should only resort to plea bargaining when they are sure Fred and William are guilty. But then trial by jury just becomes a façade under which the police really decide who gets convicted and who does not. That is not justice.
         So, why not ban plea bargaining? Plea bargaining has at least two clear merits: (i) A guilty plea negates the need for a trial with the misery that this can impose on victims. (ii) Society may want to be more lenient on wrongdoers who show genuine remorse for their wrong. Plea bargaining, therefore, is not the problem. Problems only arise if the incentives of the police or prosecution become misaligned with the desires of victims and society. That is almost certainly going to be the case in a system like the US or UK that rewards the police and prosecution for 'successful' convictions.
        So, how we can realign the incentives of the prosecution and society? This a tough question with no simple answers. It is, though, important to recognise the question exists! At the moment there does not seem an enough awareness of the issues and that is a problem for justice.  

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