Final answer:
China had the greatest influence on Korean political institutions through various aspects such as Confucianism and the Chinese writing system.
Step-by-step explanation:
The Asian country that had the greatest influence on Korean political institutions is China. Throughout history, China had significant political and cultural influence on Korea, particularly during the periods of the Three Kingdoms and the Goryeo Dynasty. Examples of China's influence include the adoption of Confucianism, the Chinese writing system, and the influence of the imperial examination system in Korean political institutions.
Learn more about The influence of China on Korean political institutions