Gerontocracy.
Gerontocracy is a form of social organization in which the elderly hold the majority of power and influence. In a gerontocracy, older people are valued for their wisdom and experience, and their accumulated knowledge and skills are highly respected. This type of political and social structure has been observed in various cultures throughout history, including Sparta, as described in the prompt. While gerontocracy is not as prevalent in modern societies, there are still some cultures where the elderly hold a significant amount of power and influence, such as in some Indigenous communities.