Skip to main content

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.  

Comments

Post a Comment

Popular posts from this blog

Revealed preference, WARP, SARP and GARP

The basic idea behind revealed preference is incredibly simple: we try to infer something useful about a person's preferences by observing the choices they make. The topic, however, confuses many a student and academic alike, particularly when we get on to WARP, SARP and GARP. So, let us see if we can make some sense of it all.           In trying to explain revealed preference I want to draw on a  study  by James Andreoni and John Miller published in Econometrica . They look at people's willingness to share money with another person. Specifically subjects were given questions like:  Q1. Divide 60 tokens: Hold _____ at $1 each and Pass _____ at $1 each.  In this case there were 60 tokens to split and each token was worth $1. So, for example, if they held 40 tokens and passed 20 then they would get $40 and the other person $20. Consider another question: Q2. D...
Post a Comment
Read more

Measuring risk aversion the Holt and Laury way

Attitudes to risk are a key ingredient in most economic decision making. It is vital, therefore, that we have some understanding of the distribution of risk preferences in the population. And ideally we need a simple way of eliciting risk preferences that can be used in the lab or field. Charles Holt and Susan Laury set out one way of doing in this in their 2002 paper ' Risk aversion and incentive effects '. While plenty of other ways of measuring risk aversion have been devised over the years I think it is safe to say that the Holt and Laury approach is the most commonly used (as the near 4000 citations to their paper testifies).           The basic approach taken by Holt and Laury is to offer an individual 10 choices like those in the table below. For each of the 10 choices the individual has to go for option A or option B. Most people go for option A in choice 1. And everyone should go for option B in choice 10. At some point, therefore, we expect the...
Post a Comment
Read more

Nash bargaining solution

Following the tragic death of John Nash in May I thought it would be good to explain some of his main contributions to game theory. Where better to start than the Nash bargaining solution. This is surely one of the most beautiful results in game theory and was completely unprecedented. All the more remarkable that Nash came up with the idea at the start of his graduate studies!          The Nash solution is a 'solution' to a two-person bargaining problem . To illustrate, suppose we have Adam and Beth bargaining over how to split some surplus. If they fail to reach agreement they get payoffs €a and €b respectively. The pair (a, b) is called the disagreement point . If they agree then they can achieve any pair of payoffs within some set F of feasible payoff points . I'll give some examples later. For the problem to be interesting we need there to be some point (A, B) in F such that A > a and B > b. In...
Post a Comment
Read more