# The General’s Dilemma

Today I am going to do “The General’s Dilemma” activity in my Intro Stats class.  I am teaching completely randomized designs, so this is a great opportunity to illustrate the methodology behind this experimental design with this activity.  This data will be used to introduce the inferential methods of comparing two independent proportions using randomization methods.  Feel free to use this in your classes.

Activity – The General’s Dilemma    The following two questions are called the first and second versions of the General’s Dilemma.  The questions were written by psychologists Daniel Kahneman and Amos Tversky.

Version I:  Threatened by a superior enemy force, the general faces a dilemma.  His intelligence officers say his soldiers will be caught in an ambush in which 600 of them will die unless he leads them to safety by one of two available routes.  If he takes the first route, 200 soldiers will be saved.  If he takes the second, there is a one-third chance that 600 soldiers will be saved, and a two-thirds chance that none will be saved.  Which route should he take?

Version II:  Threatened by a superior enemy force, the general faces a dilemma.  His intelligence officers say his soldiers will be caught in an ambush in which 600 of them will die unless he leads them to safety by one of two available routes.  If he takes the first route, 400 soldiers will die.  If he takes the second, there is a one-third chance that no soldiers will die, and a two-thirds chance that 600 soldiers will die.  Which route should he take?

(a) Do not share both versions with your students.  Randomly assign Version I to half the students in your class and Version II to the other half.    If you like, tell your students they are participating in a randomized trial and share with them how you will assign each to a treatment group.

(b) Administer the treatment (be sure each version is written on the same style and color paper).  Ask each student to record which route he or she would take: Route 1 or Route 2.  Aggregate the data for the class.

(c) Show students both versions.  Ask them to explain why Version I might be called the “Saving Lives” version and Version II the “Preventing Deaths” version.  Also, ask students to explain why Route 1 might be called the “Risk Averse” option and Route 2 the “Risk-Seeking” option.

(c) Organize the data in a two-way contingency table.  Let the row variable represent the version and let the column variable represent the route.

(d) Determine the conditional distribution of route selected by version.

(e) The research objective is to determine if there is a difference in route selected depending upon the version read.  Based on this, determine the null and alternative hypotheses.

(f) Using the randomization test for two proportions applet in StatCrunch to approximate a P-value for this hypothesis test.  Based on the result, what do you conclude?