Automated Market Makers (AMMs) operating on a decentralized system provide several benefits, including:

1. _Resistance to manipulation_: Decentralization makes it difficult for a single entity to manipulate prices, ensuring a fairer market.

2. _Censorship resistance_: Decentralized AMMs are less susceptible to censorship or shutdown by a single entity.

3. _Increased security_: Decentralized systems are more secure, as there is no central point of failure.

4. _Improved transparency_: Decentralized AMMs provide transparent pricing and trading logic.

5. _Community-driven development_: Decentralized AMMs can be open-source, allowing a community of developers to contribute and improve the system.

6. _Reduced counterparty risk_: Decentralized AMMs eliminate the risk of a single counterparty defaulting.

7. _Permissionless access_: Anyone can access and use decentralized AMMs, without needing permission from a central authority.

By operating on a decentralized system, AMMs can promote a fairer, more transparent, and more resilient market, aligning with the principles of blockchain technology and decentralized finance (DeFi).