The responsibilities of members of the Peloponnesian League primarily included:
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Providing soldiers to Sparta: Member states were expected to contribute soldiers to support Sparta's military campaigns.
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Assisting in defense: While the primary mission of the league was not specifically to defend against Persia, members were expected to support one another in military endeavors, including potential conflicts with Persia, particularly during the earlier conflicts before the Peloponnesian War.
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Autonomy and loyalty to Sparta: While members had a degree of autonomy, they were expected to align with Spartan interests and decisions in military and political matters.
The other options (such as voting on league rules and paying money to build a military) are less accurate representations of the league's functions compared to the primary responsibilities mentioned above. The Peloponnesian League was centered on Spartan hegemony, and the decisions were largely dominated by Sparta itself.