From Civ World

Promotions are earned any time a player wins a medal. Winning a medal will automatically improve the player's rank by one level, from Lord/Lady to Duke/Duchess to Prince/Princess and finally to King/Queen.

The current King/Queen will be demoted to Prince or Princess whenever another player is promoted to King/Queen, since there can be only one monarch of each Civilization.

Promotions can also occur from winning Contests or winning certain Auctions.

Ministry Promotions

Promotions to ministries work a little bit differently from promotions for rank. Each time a player of Duke/Duchess rank or higher wins a new medal, that player is automatically promoted to the ministry associated with that type of medal.

• Winning a Military medal will promote the player to Defense Minister
• Winning an Economic medal will promote the player to Finance Minister
• Winning a Culture medal will promote the player to Culture Minister
• Winning a Science medal will promote the player to Science Minister
• Winning a Construction medal will promote the player to Interior Minister
• Winning a Population medal will promote the player to Political Minister