The powerful magistrate Mark has just returned to Rome from a six-month diplomatic trip to the east. In Rome, he is met by the no less powerful magistrate Lucius. It is in Mark's interests to achieve a peaceful transfer of the province to the Eastern Empire, and Lucius seeks to return it to Rome. It is in the power of these two magistrates to elect a dictator (a ruler who is elected in Rome for a short term to solve some specific geopolitical problem and who has absolute power). There are 7 contenders for the role of dictator: Atilius, Sulla, Licinius, Messalla, Vespasian, Vindex and Grotius. Each magistrate knows the order of preference of the candidates of his vis-a-vis.

For Mark, the candidates are in this descending order of attractiveness:

1. Licinium;

2. Sulla;

3. Vespasian;

4. Vindex;

5. Grotius;

6. Messalla;

7. Atilius.

For Lucius, the descending order of attractiveness is:

1. Vindex;

2. Grotius;

3. Licinium;

4. Atilius;

5. Vespasian;

6. Sulla;

7. Messalla.

Mark proposes the following rules, invented by his wife: each player, as his proposal, can arrange all seven candidates in some order. Placement cheating is allowed. The candidate whose worst score among the two voters is the highest is selected. Mark reserves the right to be the first to place.

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