## December 22, 2004

### A Bayes Rule Classroom Game: Killers in the Bar

Your instructor has wandered into a dangerous bar in Jersey City. There are six people in there. Based on past experience, he estimates that three are cold-blooded killer and three are cowardly bullies. He also knows that 2/3 of killers are aggressive and 1/3 reasonable; but 1/3 of cowards are aggressive and 2/3 are reasonable. Unfortuntely, your instructor then spills his drink on a mean- looking rascal who responds with an aggressive remark.

In crafting his response in the two seconds he has to think, your instructor would like to know the probability he has offended a killer. Give him your estimate. Your instructor has wandered into a dangerous bar in Jersey City. There are six people in there. Based on past experience, he estimates that three are cold-blooded killer and three are cowardly bullies. He also knows that 2/3 of killers are aggressive and 1/3 reasonable; but 1/3 of cowards are aggressive and 2/3 are reasonable. Unfortuntely, your instructor then spills his drink on a mean- looking rascal who responds with an aggressive remark. In crafting his response in the two seconds he has to think, your instructor would like to know the probability he has offended a killer. Give him your estimate.

After writing the estimates and discussion, the story continues. A friend of the wet rascal comes in the door and discovers what has happened. He, too, turns aggressive. We know that the friend is just like the first rascal-- a killer if the first one was a killer, a coward otherwise. Does this extra trouble change your estimate that the two of them are killers?

This game is a descendant of the games in Holt, Charles A., \& Lisa R. Anderson. Classroom Games: Understanding Bayes’ Rule,'' {\it Journal of Economic Perspectives}, 10: 179-187 (Spring 1996), but I use a different heuristic for the rule, and a barroom story instead of urns. Psychologists have found that people can solve logical puzzles better if the puzzles are associated with a story involving people's identities. (See Dawes, Machiavellian intelligence theory).

I have the instructors' notes, which explain the answers in detail, at http://www.rasmusen.org/GI/probs/2bayesgame.pdf

Posted by erasmuse at December 22, 2004 03:30 PM