I. You have been for many years the absolute ruler of a small oil producing country in North Africa, loved and admired by your grateful subjects.  Recently dissident elements, no doubt in the pay of foreign enemies and encouraged by the overthrow of the ruler of a neighboring nation, have been holding demonstrations against you, demanding free elections. You are considering three alternatives:

1.     Announce that, due to the peace, order, prosperity and widespread education produced by your long and enlightened rule, you can now lay down the burdens you have so long borne and retire.

2.     Proclaim a new constitution, permitting opposition parties to organize and run candidates, with  elections to be held in three months, and announce that you will be a candidate for president and that your party will run a slate of candidates for lower offices.

3.     Announce that the demonstrators are criminals, drug addicts, and foreign mercenaries, and will be put down by your loyal police and army, using as much force as necessary.

While alternative 1 appears the least risky, there is a possible down side. You estimate that there is a 25% chance that, after you give up power, your successor will successfully demand that foreign governments freeze the assets that you have accumulated through your hard work and careful saving, leaving you with a mere hundred million dollars, prudently concealed under other names, to support yourself and your family. Worse still, there is an additional 10% chance that relatives of some of the criminals you executed during your reign will accuse you of past wrongdoing and succeed in having you extradited, tried, and imprisoned. After spending a few days contemplating these alternatives, you set the following values on them:

Safe retirement: $1 billion

Retirement with a remnant of your wealth: $100,000,000.

Extradition, conviction, and imprisonment: 0

Before making your decision, you hire a polling firm to estimate the chance that you and your party can win a free election. To your surprise, they conclude that there is only a 40% chance of success. If you succeed you believe that, over the next few years, you will be able to use your loyal supporters in the Security Services to eliminate the opposition parties and restore the situation as it existed before the recent troubles. If you lose, you plan to retire in safety.

At this point, a loyal supporter in the Security Service brings you some disturbing news. The head of the service, Abdul “Butcher” al-Hakkar, worried about the consequence to himself if you hold an election and lose it, plans to seize power if that happens; the first step in such a coup will be to have you killed by one of your bodyguards. You believe that your chance of getting safely out of the country in that situation is only 50%. Your values for these outcomes are:

Win the election and reestablish your rule: $3 billion (you like being an absolute ruler)

Lose the election and retire: $1 billion

Lose the election and be killed: 0

It occurs to you that, immediately before announcing elections, you could invite Abdul into your office and shoot him, reporting his death as the result of a failed attempt to prevent the introduction of democracy to your nation. Doing so will eliminate the risk of  coup and increase your popularity, raising the chance of winning the election to 60%. Unfortunately, there is a 25% chance that Abdul will realize what you are doing and get his shot off first, killing you. Your value for this outcome is 0.

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The third alternative is now looking increasingly attractive. You estimate that you have a 50% chance of successfully suppressing the opposition and restoring your rule. Doing so, however, will require killing large numbers of demonstrators, creating a great deal of bad publicity abroad and hostility at home from the survivors. You estimate the value of that outcome at $2 billion. If your efforts fail, you are unlikely to survive, but at least you will have the satisfaction of having died fighting heroically, a martyr to your cause. You value that outcome at $200 million.    (15 points)

Use decision analysis to diagram your choices and identify the most attractive. For simplicity, assume you are risk neutral.

(Use the back of the previous page if necessary)