Expected Utility

Sun Tzu anticipated Expected Utility with the advice, “If it does not profit the state, do not deploy your armies. If the objective cannot be seized, do not give battle.” Bueno de Mesquita’s (1981, 1992) “Expected Utility Theory” grew out of the Correlates of War project.

· Decision makers are instrumentally rational.⁵ They can order or rank, but need not be able to rate, their preferences

· Decision makers consider options in terms of probabilities associated with possible outcomes multiplied by utilities associated with those outcomes.

· Decision makers choose the option with the highest expected utility.

The equation for the expected utility of a challenge to the existing policy is:

Where:

E(U)_c = expected utility of challenging the policy

P_s = probability of successful challenge

U_s = utility of successful challenge

U_f = utility of failed challenge

The equation for the expected utility of not challenging the status quo is:

Where:

E(U)_nc = expected utility of not challenging the policy

P_q = probability that the policy will not change

U_q = utility of the policy

P_b = probability that the policy will change with positive utility

U_b = utility of a positive policy change

U_w = utility of a negative policy change

The overall expected utility is the difference between the two equations:

If E(U) is greater than 1, it is rational to initiate a war. That is, a necessary, but not a sufficient, condition for starting a war is that the expected utility of victory must be greater than the expected utility of defeat.

De Mesquita initially tested his ideas by using the Correlates of War data for 251 conflicts and crises from 1816 to 1974, limiting his analysis to cases in which the initiator was clear. He incorporated both attitude toward risk and relative power into the formula to determine utility after considerable ingenuity developing ways to estimate each.

Initiators won 75% of their wars. In most cases that they lost, the formula results in a negative utility. That is, the leader made a mistake in choosing war. Of the remaining cases, the expected utility score is so close to zero that it is within the margin of error. None of this should come as a surprise. Most leaders do not go to war lightly, although their reasons for accepting or avoiding the risk and the amount of risk they can tolerate may vary considerably.