Rama Menon

Spring 2003
The Prisoners' Dilemma

I have read John Allen Paulos’ “Innumeracy” many times, and each time I read it, I get an epiphany, and am amazed at how much he covers in that 180 page book.  On a recent reading of it, I was struck by what he discusses in chapter 5, entitled “Statistics, Trade-Offs, and Society,” and thought that one of the examples in that chapter, called the “prisoners’ dilemma,” might be worth discussing in the “Musings” column.  But before I explore the “prisoners’ dilemma,” I would like to take a look at an economic model, also discussed by Paulos.

According to one version of Adam Smith's economics, if each individual seeks to maximize his or her own wealth, then the wealth of all will be maximized.  This is akin to the sum of the parts being equal to the whole.  But we know that in many instances, the aggregated parts do NOT sum up to a whole.  For example, even if a person can perform all the different progressions of a tennis skill, such as the serve, there is no guarantee that in any given game, he or she can execute a flawless serve.  Similarly, a foreign student may know all the parts of a sentence, but may not be able to string together words to form a contextually meaningful sentence.  In math, there can be instances of ratios, where the sum of the ratios (as in batting averages for a whole year, etc.), may be less than an individual ratio (as in batting averages for a particular season).  Or, perhaps, students might be able to recite the times table accurately, but may not be able to use multiplication in a given situation such as a word problem.

Because there are so many instances where the sum of the parts is not necessarily the whole, we might posit that this might also be the case for Adam Smith’s economic model of individual pursuit of wealth through hard work resulting in the well-being of society as a whole.  In other words, working towards one’s self interest, might, in the long run, work against one’s self interests-and that is the basis of the prisoners’ dilemma.

The prisoners’ dilemma is usually given in the following context: two men are suspected of serious crimes but arrested for a minor crime, thereby becoming prisoners.  They are separated and questioned, and each is given a choice: either confess to the serious crimes, and state both of them were involved, or remain silent.  If both remain silent, each will get a jail term of one year.  If one confesses, and the other doesn’t, the one who confesses will be set free, and the other will be given a five-year jail sentence.  If both confess, each will do a three-year jail term.

Assume I am one of the prisoners.  Then my dilemma is this: If I confess and implicate my partner, that leaves me open to either my partner remaining silent (in which case I go free, and he gets five years), or my partner, too confessing and implicating me (in which case both of us will get three years).  But if I remain silent, that leaves me open to my partner also remaining silent (in which case both of us will go free), or my partner confessing and implicating me (in which case he goes free, and I get five years).  If I choose to look only after my own welfare, I might choose the option of confessing, and implicating him, in which case I will either go free if he chooses to remain silent, or I will get three years, if he, too confesses and implicates me.  So, in either case, my selfish/individualist option would be to confess and implicate him.

Hence, the selfish option-that is looking out for oneself--(from each prisoner’s perspective) would result in either a three-year or five-year term in jail.  But if each of them were to remain silent, then both will get only a one-year jail term.  Hence, the cooperative option that brings about the most good for both of them would be to remain silent.  But the dilemma is that there is no guarantee that if one remains silent, the other, too, will remain silent, and so, would it not be better to confess and implicate the other, so as to either go free, or get three years?

The prisoners’ dilemma discussed here represents many everyday situations (for example, decisions by spouses, businesses, the UN Security Council, etc.) where a choice has to be made, either for the common good, or for an individual’s selfish interests.  In other words, when two parties get together to discuss an issue, the cooperative decision would be to come to a compromise, where neither party gets all that was initially wanted, but each gets part of what was wanted.

I reiterate that the prisoners’ dilemma is a good example of the use of logic in some everyday situations, as opposed to its use in some abstract academic situations.  It seems to me, too, that both policy makers and other stakeholders might profit from a discussion of the prisoners’ dilemma when looking at some of the latest decisions on what is considered acceptable research (“scientifically-based research”), or what is considered important criteria for accountability and student learning (“high stakes standardized testing”).

Any thoughts on the wider applicability (or lack of applicability) of the prisoners’ dilemma are welcome!