A military operation is planed with the outcomes being in order from best to wor

Question

A military operation is planed with the outcomes being in order from best to worst) a complete succes (C, a substantial success (S), a partialsuccess (P), and a fallure (F). Itis of course also possible to do nothing (D)-that decision is not considered to be either the best or the worst. The commander is faced with the following decision wherethe outcome is affectedlargely by weather. The weatheris dlassfied as very bad Vi, bad (B) fair (F and good (G), with the probablities given in the diagram below C (BestOutcome) F (3) V(F(Worst Outcome) go dont go The commander is indifferent between the following lotteries 15 85 a. (1.5 points each) What is the utility for each outcome (C, ,P,D) b. (1.5 points) What decision should the commander make, based on expectedutlity?

Explanation / Answer

a)

Utility of C = 1

Utlity of F = 0

Utility of S = 0.7*1+0.3*0 = 0.7

Utility of P = 0.15*1+0.85*0 = 0.15

Utility of D = 0.4*0.7+0.6*0.15 = 0.37

b) Expected utility of go decision = 0.4*1 + 0.3*0.7+0.2*0.15+0.1*0 = 0.64

Expected utility of don't go decision = 0.37

Expected utility of go decision is higher. Therefore, commander should go ahead with the operation.

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