Q.Using the payoff table of Worked Example 6, suppose the probabilities are revised to $P(S_1)=0.5$, $P(S_2)=0.3$, $P(S_3)=0.2$. Compute the EMV of each action and state which action should be chosen. Comment on your result.

Recomputing EMV with a different, but still valid, set of probabilities on the very same payoff table can change which action comes out ahead — here it produces a genuine tie between two actions rather than a single clear winner. …

Using the same payoff table — $A_1=(200,200,200)$, $A_2=(100,300,300)$, $A_3=(50,200,400)$ — with the revised probabilities $P(S_1)=0.5, P(S_2)=0.3, P(S_3)=0.2$:

$A_1$ and $A_2$ are exactly tied at an EMV of ₹200 ('000), both ahead of $A_3$ at ₹165.

Cross-check using EOL: expected payoff under perfect information $=200(0.5)+300(0.3)+400(0.2)=100+90+80=270$. Using the regret table — $A_1=(0,100,200)$, $A_2=(100,0,100)$, $A_3=(150,100,0)$:

$EOL(A_1)=EOL(A_2)=70$, confirming the same tie found by EMV, and $EVPI=270-200=70$ matches this minimum EOL exactly, so the calculation is internally consistent. …

Assuming EMV calculations must always produce a single clear winner — a genuine tie is a valid result, and simply means the decision-maker is indifferent between those two actions on EMV grounds alone …