The Little Blue Reasoning Book - Brandon Royal [24]
Now view this same example in terms of the reverse hypothesis: “I have cancer.” In this case, with reference to the following matrix, suppose the hypothesis is true and we reject it (thus committing a Type I error). Now suppose the hypothesis is incorrect and we accept it (thus committing a Type II error). This time the Type I error is more serious for the identical reason cited in the previous scenario.
In summary, all research propositions should be analyzed in this manner. We should ask: If the hypothesis is true, what are the consequences of rejection? If the hypothesis is false, what are the consequences of acceptance? Depending on our answer, we will risk committing one error more than the other.
Note that Type I and Type II errors are discussed with more frequency with respect to medical situations, where the impact of such errors is more serious. In other situations, as seen in the previous examples titled Political Beliefs and Stockbrokers, these two types of errors are not nearly as critical.
PRISONER'S DILEMMA
Tip #19: The Prisoner’s Dilemma provides an example of how cooperation is superior to competition.
Once upon a time, the police caught two suspects with ample counterfeit notes in their possession. The police knew the two men were acquaintances and escorted them to separate jail cells so they couldn’t connive. The police knew the men were working in collusion but couldn’t find the counterfeiting machine after a thorough search of each of their premises. Without more solid evidence, the police knew the suspects would receive light sentences, as they had semi-plausible alibis.
Indeed, a confession was needed. The police decided to offer immunity to the first suspect who confessed and also offered up the location of the counterfeiting machine. This person would go free, and the other suspect would get a 10-year prison sentence. If they remained silent, they could each expect a three-year prison sentence for possession of multiple counterfeit bills. Each suspect was also told, out of judicial fairness, that if they both confessed they would each receive a seven-year prison sentence.
Each suspect faced four possible outcomes:
If you were one these suspects, what would you do?
First you might consider what your partner will do. Let’s say the you both decide to keep quiet. If you keep quiet too, you get three years; if you confess, you go free. Thus, it’s better for you to confess when your partner keeps quiet — you go free.
But what if he confesses? Now if you keep quiet, you get ten years; if you confess, you get seven years. Thus, if he confesses, it’s also better for you to confess (results in three fewer years). Regardless of what he does, you avoid three years in jail by confessing.
It sounds like you should confess. The hitch — a big hitch — is that if he figures things out the same way, he’s going to confess — just like you — and you will both get seven years, even though you both could have kept quiet and only received three years each.
This situation is called the Prisoner’s Dilemma. The story was first told by economist A.W. Tucker in 1950. The police have probably known this game for a long time. So have criminals. It is just one version of a simple but compelling bargaining game.
The Prisoner’s Dilemma is an example of a mixed-motive game: Both parties can do well if they work together by cooperating or they can try to gain an advantage over each other by competing. The fact that elements of both cooperation and competition are simultaneously present makes for mixed motives and contributes to the inherent complexity in these and similar games.
The Prisoner’s Dilemma game is also an example